Support the production of this course by joining Wrath of Math as a Channel Member for exclusive and early videos, original music, and upcoming lecture notes for the graph theory series! Plus your comments will be highlighted for me so it is more likely I'll answer your questions! th-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin Graph Theory course: th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html Graph Theory exercises: th-cam.com/play/PLztBpqftvzxXtYASoshtU3yEKqEmo1o1L.html
Thank you for taking the time to share your knowledge. Graph C & D are not isomorphic since the number of vertices are not same. Graph A & B are isomorphic as they have same number of vertices and edges, the degree of each of the vertices in both graphs is same ( 2 ) and a bijective function linking both the graphs is possible.
Thanks for watching and right on! Graphs A and B have the same number of vertices and edges, and the same vertex degrees, which isn't enough to conclude they are isomorphic, but it does suggest they might be. Then, as you said, a bijective function exists between the graphs that preserves adjacency and nonadjacency. I believe I typed out an example of such a bijection in the description for anyone curious.
Well that was a brilliant explanation..easy to understand . A and B are isomorphic ( because same number of vertices and there are exist bijective function as well) While C and D are non isomorphic (As it doesn't have same number of vertices and and bijective function is not possible.)
This is by far the best explanation I’ve come across. I have autism and memory issues which interfere with my ability to understand abstract concepts and picture things like this in my head. Your use of plain English words and examples really helped!
This helped me with understanding people that don't speak in plain English: Analogies that correctly communicate an idea are isomorphic to the idea. Analogies that fail to communicate an idea are not isomorphic. Sus out the objects (the vertices) and the relationships (the edges) and then map their analogies to the plain english that makes sense to you. Then communicate your version back to them. If they confirm your version is the same as theirs, then the isomorphism has been achieved and the idea has been communicated.
Thank you for this. I am still in my undergraduate studies for Education majoring in Math, but we are required to have a thesis and Graph Theory is the one who captured my attention. For my answer, Graph A and B are isomorphic since it satisfies the presence of Bijection and also for simpler explanation the 2 graphs are just Cyclic graphs of C5. For C and D graphs, non-isomorphic since the number of vertices don't match from graph C and graph D.
Thanks so much, Masudur! I do my best, and I'm so glad you've found my explanations helpful. If you're looking for more graph theory, check out my playlist, and let me know if you ever have any questions! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Thank you! it is really a good vieo. you explained very clearly. I think Graph A and B is isomorphic, because 1.They both have 5 vertices and 5 edges 2. each of their vertices has two adjacencies V(A)→ V(B) 𝜑 v1 v2 v3 v4 v5 u1 u4 u3 u2 u5 so they are bijective 3. v1 v2 ∈E(H) and 𝜑 (v1)𝜑 (v2) ∈E(H) For graph C and D, they are not isomorphic, because they don't have same vertices and edages
So glad it helped, thanks for watching! Check out my graph theory playlist if you're looking for more: th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html Lots of lessons left to come!
So glad you liked it, thanks for watching! If you're looking for more graph theory, check out my playlist! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html I will make a discrete math playlist at some point, but for now there is plenty of graph theory!
Thank you! I try to make concepts as clear as I can. If you're looking for more graph theory, check out my playlist! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Thank you so much Sean. Your lectures are really helpful. You convey everything properly in a very short time. I can listen to your lectures all day and won't get tired😂 Can you please make a video on Arboricity, linear arboricity and related topics/Theorems like Nash-Williams theorem!?
Thanks so much for watching, Ramsha! There is still a lot of graph theory for me to cover to complete this playlist, but I am glad it has been helpful. I'd love to cover that stuff, unfortunately it would take a while and is a very niche topic. I can't really justify the time for it right now, but if you have any specific questions on that material feel free to shoot me a message!
@@WrathofMath it’s good to hear back from you within 48 hours😊 I am actually studying this topic currently but your lecture on this would have been of great help. I revised and learned almost all GT basics from your videos. I understand you must be busy. I will surely ask for help whenever needed. Thank you so much. God bless you🌻
@@WrathofMath arboricity of a graph is actually minimum number of forests into which its edges can be partitioned. But I want to understand that partition through some examples. How do we do partition of a graph into forests!? What would be the rules to follow here!? Please answer for them whenever you have time. Tc😊
Watched another video on this and determined I would have to study various abstract theories to get to the point of understanding isomorphism (since I looked this up due to php coding not from mathematical theory) then found yours and it made sense. TY!
Thank you! Be sure to check out my Graph Theory playlist if you haven't many more lessons to come! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
The music at the very end scared the shit out of me it sounded like it was coming from outside of my headphones at first. Thank you for your explanation here I am going to use it to help me on my Algorithms and Data Structures homework
So glad to help! Thanks for watching, and if you're looking for more graph theory check out my playlist! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Injective means One-To-One. Surjective means Onto. At 5:18 in the video, you say that "Injective" and "Surjective" combined implies a One-To-One correspondence but One-To-One is only associated with "Injective". It is true that the graph is One-To-One and Onto but I don't think the combination of "Injective" and "Surjective" means "One-To-One". Only the "Injective" is required for "One-To-One." The "Surjective" is not necessarily required for "One-To-One". Is this a mistake in the video or am I missing something? Please advise, thank you.
Great question! It is confusing, but this is how the phrases are used. Everything you said is right, but one to one correspondence is different from one-to-one. Injective: One to one (each one input has its own one output, not shared by any other input) Surjective: Onto (the function maps the domain onto the entire codomain, every element of the codomain gets mapped onto by some domain element) Bijective: One-to-one correspondence (the domain and codomain correspond exactly - one to one - every domain element corresponds to one codomain element and vice versa) Hope that helps!
@@WrathofMath That makes perfect sense. I had clumsily assumed One-To-One and One-To-One Correspondence were the same thing. Thanks so much for the explanation and the playlist!!
First of all, thank you for making videos on Graph Theory! The videos really help in driving the concepts home! Secondly, if given two graphs which have a lot of vertices (say around 20) and you are asked to check for isomorphism, how would you proceed with it? I did see a video before this that said you also needed to check the degree sequence but isn't checking the degree sequence for 20 vertices a bit impractical since the edges can make things a little bit confusing?
A policeman (red diamond) runs after a thief (green square) in the diagram above according to the following rules: • The 2 players are obliged to move in turn; • The policeman moves first; • A player can only move following an arc, and he can only move from a distance from a peak of its original position; • The policeman seeks to catch the thief (that is to say that the 2 are on the same summit) a) Find a strategy for the police to catch the thief. b) Explain why the strategy works all the time
A and B are isomorphic, phi: map v1 to u2, v5 to u3, v4 to u4, v3 to u1, v2 to u5. Sort of pick any vertex and follow the pack where it‘s edges takes you.
i have a doubt in regards to the A and B pair of examples in the end, i believe that they are not isomorphic because, yes, they have the same number of vertices and edges, but it doesnt preserve adjacency correctly, in A v1 and v2 are adjacent to each other and in B they aren't, there are some other cases of that in those graphs.This is assuming that the isomorphisim takes the vertices v1 to u1, v2 to u2, so on and so forth. I hope i´m okay on that observation.
Thanks for watching and for the question! I'm not sure what you mean by "it" doesn't preserve adjacency correctly. What is "it"? Remember in order for graphs A and B to be isomorphic, there must be an isomorphism between them, and that's the thing preserving adjacency. So, to be sure that A and B are isomorphic, we need to find an isomorphism between them, but I simply drew the graphs on screen and did not provide an isomorphism. So the exercise is to either determine they are not isomorphic and a reason why, or if you think they are isomorphic, to find an isomorphism between them. The vertices of A are labeled v1 through v5, and the vertices of B are labeled u1 through u5, but there is no isomorphism given. Does that make sense?
Haha, glad to be able to help! If you haven't already, check out the graph theory playlist: th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html Everything is pretty well organized in it for your convenience. I'll be making a general discrete math playlist eventually, but it will take time! Let me know if you ever have any video requests!
Thank you. Well explained (y) A and B are isomorphic because if you can unfold the star and you get the same structure (visually) as the pentagon. C and D are not isomorphic, there's not vertex with 4 edges in D, so there's a pare of vertices that will be adjacent in C but not D.
So glad to help with such an important topic! Thanks for watching and check out my graph theory playlist if you're looking for more! Thanks for watching, graph theory can indeed be hard! Let me know if you have any questions I can help clear up, and check out my playlist if you're looking for more graph theory videos that may solve some of your problems: th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Thanks for watching and for the request Charles! I'd love to make a video on automorphisms soon, but no promises! If you haven't already, check out my graph theory playlist for more! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Glad to hear it, thanks a lot for watching! If you're looking for more graph theory, check out my playlist! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
I watched a video of @sarada_herke about finding isomorphism between two graphs using their adjacency matrices but I still have a doubt about finding the correct permutation matrix since there are n! distinct permutation matrices for a graph with n vertices. Please help me with this problem.
Thank you Sean for the great explanation! So if a maximum degree between 2 graphs differs then they are not isomorphic right? another question if the longest path of the first graph has different length from the longest path in the second graph then they are not isomorphic?
Thanks for watching and that's exactly right! All those sorts of properties that don't depend on the names of the vertices will be present among isomorphic graphs. If G and H are isomorphic, and G has a vertex v, with G's maximum degree of 5, then the image of v in H under the isomorphism must have just as many neighbors, and thus the same degree. Say the isomorphism is f, and so the image of v in H is f(v). Then the neighbors of v in G will necessarily have images in H that are all adjacent to f(v). More detailed explanation: th-cam.com/video/b7HHyhBboKk/w-d-xo.html
Thanks for watching and the request! I'm looking at the book, it has some cool stuff on the Petersen graph, I'll make some videos on some of it! Currently I don't have much time to do all the prep for longer detailed lessons, which require a lot of organization of ideas. But I'll do what I can!
@@WrathofMath Can you do a video on strong induction and non-homogenous recurrence relations? I love the way you explain everything. I have a really hard time understanding these two concepts.
A & B are isomorphic: 5 verts, all verts have 2 edges, both graphs have 5 Hamiltonian Circuits each with 5 steps. C is not isomorphic to any because it has a vert with 4 edges while no other graph has a vert with 4 edges. D is not isomorphic because it has 4 verts while all others have 5 verts.
A and B are not isomorphic - Same number of vertices - Same number of edges - Same sequence of vertex degrees - Same edge connections (i.e., adjacency matrix) But differing only in planarity (one is planar, and the other is non-planar)
Support the production of this course by joining Wrath of Math as a Channel Member for exclusive and early videos, original music, and upcoming lecture notes for the graph theory series! Plus your comments will be highlighted for me so it is more likely I'll answer your questions!
th-cam.com/channels/yEKvaxi8mt9FMc62MHcliw.htmljoin
Graph Theory course: th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
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Thanks
First 50 seconds already told me more than a 16 page section in a math book... thank you sir.
You're very welcome and thank you! I am glad it helped and let me know if you ever have any questions!
verbose topic xD
Now pass an exam with only this video as guide.
i like the speed of teaching , very precise ,very clear and to the point with revision.....omg..
Thanks so much! I am glad it helped and let me know if you ever have any questions!
I love how easily you simplified the concept by breaking it down into further smaller topics. You are insane
Thank you for taking the time to share your knowledge.
Graph C & D are not isomorphic since the number of vertices are not same.
Graph A & B are isomorphic as they have same number of vertices and edges, the degree of each of the vertices in both graphs is same ( 2 ) and a bijective function linking both the graphs is possible.
Thanks for watching and right on! Graphs A and B have the same number of vertices and edges, and the same vertex degrees, which isn't enough to conclude they are isomorphic, but it does suggest they might be. Then, as you said, a bijective function exists between the graphs that preserves adjacency and nonadjacency. I believe I typed out an example of such a bijection in the description for anyone curious.
@@WrathofMath are all complimentary graphs isomorphic as well?
Well that was a brilliant explanation..easy to understand .
A and B are isomorphic ( because same number of vertices and there are exist bijective function as well)
While C and D are non isomorphic (As it doesn't have same number of vertices and and bijective function is not possible.)
This is by far the best explanation I’ve come across. I have autism and memory issues which interfere with my ability to understand abstract concepts and picture things like this in my head. Your use of plain English words and examples really helped!
This helped me with understanding people that don't speak in plain English:
Analogies that correctly communicate an idea are isomorphic to the idea.
Analogies that fail to communicate an idea are not isomorphic.
Sus out the objects (the vertices) and the relationships (the edges) and then map their analogies to the plain english that makes sense to you. Then communicate your version back to them. If they confirm your version is the same as theirs, then the isomorphism has been achieved and the idea has been communicated.
Thanks for taking time to teach us the difficult subjects in a simplified way
Glad to help!
this is by far the best video on this topic available on the internet
Thanks so much!
Thank you for this. I am still in my undergraduate studies for Education majoring in Math, but we are required to have a thesis and Graph Theory is the one who captured my attention. For my answer, Graph A and B are isomorphic since it satisfies the presence of Bijection and also for simpler explanation the 2 graphs are just Cyclic graphs of C5. For C and D graphs, non-isomorphic since the number of vertices don't match from graph C and graph D.
You have become one of the best teacher in my list of the best teachers
Thanks so much, Masudur! I do my best, and I'm so glad you've found my explanations helpful. If you're looking for more graph theory, check out my playlist, and let me know if you ever have any questions! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Thank you! it is really a good vieo. you explained very clearly.
I think Graph A and B is isomorphic, because
1.They both have 5 vertices and 5 edges
2. each of their vertices has two adjacencies
V(A)→ V(B)
𝜑 v1 v2 v3 v4 v5
u1 u4 u3 u2 u5
so they are bijective
3. v1 v2 ∈E(H) and 𝜑 (v1)𝜑 (v2) ∈E(H)
For graph C and D, they are not isomorphic, because they don't have same vertices and edages
a work of art, you deserve my tuition
Crystal clear explanation than my over priced university lecture.
Thanks for this. Been trying to understand this thing for a week now and now I finally got it
Awesome, glad it helped! Thanks for watching!
thank you so much for this nice explanation now i knew how isomorphic work by easy way
So glad it helped, thanks for watching! Check out my graph theory playlist if you're looking for more: th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Lots of lessons left to come!
Loved this video, thank you very much!
I wish my Discrete Math teachers had the ability to explain things like you.
So glad you liked it, thanks for watching! If you're looking for more graph theory, check out my playlist! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
I will make a discrete math playlist at some point, but for now there is plenty of graph theory!
this is one sexy explanation of isomorphic graphs thanks.
You have the beauty of symplification I has been looking for 🙏
Thank you! I try to make concepts as clear as I can. If you're looking for more graph theory, check out my playlist! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Thank you so much Sean. Your lectures are really helpful. You convey everything properly in a very short time. I can listen to your lectures all day and won't get tired😂
Can you please make a video on Arboricity, linear arboricity and related topics/Theorems like Nash-Williams theorem!?
Thanks so much for watching, Ramsha! There is still a lot of graph theory for me to cover to complete this playlist, but I am glad it has been helpful. I'd love to cover that stuff, unfortunately it would take a while and is a very niche topic. I can't really justify the time for it right now, but if you have any specific questions on that material feel free to shoot me a message!
@@WrathofMath it’s good to hear back from you within 48 hours😊 I am actually studying this topic currently but your lecture on this would have been of great help. I revised and learned almost all GT basics from your videos. I understand you must be busy. I will surely ask for help whenever needed. Thank you so much. God bless you🌻
@@WrathofMath arboricity of a graph is actually minimum number of forests into which its edges can be partitioned. But I want to understand that partition through some examples. How do we do partition of a graph into forests!? What would be the rules to follow here!? Please answer for them whenever you have time. Tc😊
Watched another video on this and determined I would have to study various abstract theories to get to the point of understanding isomorphism (since I looked this up due to php coding not from mathematical theory) then found yours and it made sense. TY!
So glad it helped, thanks for watching!
This video hits different. Keep it up!!!
Thank you! Be sure to check out my Graph Theory playlist if you haven't many more lessons to come! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
AMEN to you my guy! First few seconds and, VOILA! MAGIC!
So glad it helped!
The music at the very end scared the shit out of me it sounded like it was coming from outside of my headphones at first. Thank you for your explanation here I am going to use it to help me on my Algorithms and Data Structures homework
Thanks for watching and I am glad it helped! And haha, sorry about the scare with the music!
Thank you for this easy and wonderfully explained video.
So glad to help! Thanks for watching, and if you're looking for more graph theory check out my playlist! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
As always, thank you for your informative videos :)
My pleasure! Thanks for watching! :)
Injective means One-To-One.
Surjective means Onto.
At 5:18 in the video, you say that "Injective" and "Surjective" combined implies a One-To-One correspondence but One-To-One is only associated with "Injective".
It is true that the graph is One-To-One and Onto but I don't think the combination of "Injective" and "Surjective" means "One-To-One".
Only the "Injective" is required for "One-To-One."
The "Surjective" is not necessarily required for "One-To-One".
Is this a mistake in the video or am I missing something?
Please advise, thank you.
Great question! It is confusing, but this is how the phrases are used. Everything you said is right, but one to one correspondence is different from one-to-one.
Injective: One to one (each one input has its own one output, not shared by any other input)
Surjective: Onto (the function maps the domain onto the entire codomain, every element of the codomain gets mapped onto by some domain element)
Bijective: One-to-one correspondence (the domain and codomain correspond exactly - one to one - every domain element corresponds to one codomain element and vice versa)
Hope that helps!
@@WrathofMath
That makes perfect sense.
I had clumsily assumed One-To-One and One-To-One Correspondence were the same thing.
Thanks so much for the explanation and the playlist!!
Thank you very much for this video. It was really useful, and simply explained. It helped me to fill the gaps at this point. Thanks again
Glad to help! Thanks for watching!
Execelent explanation bro.I understood each and every word.Thanks for the video
Glad to hear it, thanks for watching!
First of all, thank you for making videos on Graph Theory! The videos really help in driving the concepts home!
Secondly, if given two graphs which have a lot of vertices (say around 20) and you are asked to check for isomorphism, how would you proceed with it? I did see a video before this that said you also needed to check the degree sequence but isn't checking the degree sequence for 20 vertices a bit impractical since the edges can make things a little bit confusing?
A policeman (red diamond) runs after a thief (green square) in the diagram above according to
the following rules:
• The 2 players are obliged to move in turn;
• The policeman moves first;
• A player can only move following an arc, and he can only move from a distance
from a peak of its original position;
• The policeman seeks to catch the thief (that is to say that the 2 are on the same summit)
a) Find a strategy for the police to catch the thief.
b) Explain why the strategy works all the time
Very easy to understand❤❤❤❤ love this video
Thanks alot for the knowledge..... It's easy to understand ur explanations
My pleasure, thanks for watching!
Brilliant video. Thank you!
Thank you! So glad it helped, this is one of my favorites.
Would you please make a vide on the differences between automorphic, isomorphic, and homomorphic graphs?
A and B are isomorphic, phi: map v1 to u2, v5 to u3, v4 to u4, v3 to u1, v2 to u5. Sort of pick any vertex and follow the pack where it‘s edges takes you.
Clean explanation. Very nice.
Thank you! Glad it was clear!
Sir...One more doubt....In the graph C( bow graph), Can we say vertex a and vertex c are adjacent vertices?
no!,no edge betwwen them
i have a doubt in regards to the A and B pair of examples in the end, i believe that they are not isomorphic because, yes, they have the same number of vertices and edges, but it doesnt preserve adjacency correctly, in A v1 and v2 are adjacent to each other and in B they aren't, there are some other cases of that in those graphs.This is assuming that the isomorphisim takes the vertices v1 to u1, v2 to u2, so on and so forth. I hope i´m okay on that observation.
Thanks for watching and for the question! I'm not sure what you mean by "it" doesn't preserve adjacency correctly. What is "it"? Remember in order for graphs A and B to be isomorphic, there must be an isomorphism between them, and that's the thing preserving adjacency. So, to be sure that A and B are isomorphic, we need to find an isomorphism between them, but I simply drew the graphs on screen and did not provide an isomorphism. So the exercise is to either determine they are not isomorphic and a reason why, or if you think they are isomorphic, to find an isomorphism between them. The vertices of A are labeled v1 through v5, and the vertices of B are labeled u1 through u5, but there is no isomorphism given. Does that make sense?
great video, thanks for getting me through my discrete maths course xd
Haha, glad to be able to help! If you haven't already, check out the graph theory playlist: th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Everything is pretty well organized in it for your convenience. I'll be making a general discrete math playlist eventually, but it will take time! Let me know if you ever have any video requests!
Thank you. Well explained (y)
A and B are isomorphic because if you can unfold the star and you get the same structure (visually) as the pentagon.
C and D are not isomorphic, there's not vertex with 4 edges in D, so there's a pare of vertices that will be adjacent in C but not D.
beautiful explanation, thanks!
Thanks for watching!
long live to geniuses. you made life easier for me
So glad to help with such an important topic! Thanks for watching and check out my graph theory playlist if you're looking for more! Thanks for watching, graph theory can indeed be hard! Let me know if you have any questions I can help clear up, and check out my playlist if you're looking for more graph theory videos that may solve some of your problems: th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Great video, keep it up!
Amazing Video,Thank youuu❤
You're welcome, thanks for watching!
Thank you! It really helped.
Dude, Can ya make a video on Automorphism. It would be helpful.
Thanks for watching and for the request Charles! I'd love to make a video on automorphisms soon, but no promises! If you haven't already, check out my graph theory playlist for more! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Thank you sir. Great channel!
Thank you Jane! I do my best, let me know if you ever have any video requests!
thanks u very much Mahmoud from Egypt
You're very welcome! Thanks for watching, Mahmoud!
So helpful!!
Glad to hear it, thanks a lot for watching! If you're looking for more graph theory, check out my playlist! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Thank you for the explanation. What is the exit music? It sounds really good!
I know it's one of Vallow's songs, but which one?
"But officer, I thought it was okay to go through the red light; it has the same one-point structure as the green light."
Thank you sirr, well explained
Thank you!
that was a really good video tysm
Glad to help!
video request : maximum matching and max flow algorithm in bipartite graph
Sweeeeet, great explanation.
Glad it was clear, thanks for watching!
Could you please make an effort on Optimal profix code problems? Thanks
could you do more on motifs?
Is there possible of self loop in isomorphic graphs
I watched a video of @sarada_herke about finding isomorphism between two graphs using their adjacency matrices but I still have a doubt about finding the correct permutation matrix since there are n! distinct permutation matrices for a graph with n vertices. Please help me with this problem.
Thank you Sean for the great explanation! So if a maximum degree between 2 graphs differs then they are not isomorphic right? another question if the longest path of the first graph has different length from the longest path in the second graph then they are not isomorphic?
Thanks for watching and that's exactly right! All those sorts of properties that don't depend on the names of the vertices will be present among isomorphic graphs. If G and H are isomorphic, and G has a vertex v, with G's maximum degree of 5, then the image of v in H under the isomorphism must have just as many neighbors, and thus the same degree. Say the isomorphism is f, and so the image of v in H is f(v). Then the neighbors of v in G will necessarily have images in H that are all adjacent to f(v). More detailed explanation: th-cam.com/video/b7HHyhBboKk/w-d-xo.html
Please make a detailed video on petersen graph. Especially I'm getting trouble to understand it properly from the book by Douglas B. West, page 13.
Thanks for watching and the request! I'm looking at the book, it has some cool stuff on the Petersen graph, I'll make some videos on some of it! Currently I don't have much time to do all the prep for longer detailed lessons, which require a lot of organization of ideas. But I'll do what I can!
@@WrathofMath thanks a lot
how did you teach such that? it was crazy and easy to understand, ty sir
Video idea (Please :D :D): applications of Isomorphic graphs inC omputer science
Nice demonstration
Thanks, Arish!
better than the lecturer im paying 9k for
That's too bad - but I appreciate it!
Can you do a video on matrices in graph theory
how do we determine the graph isomophism falls under P or NP?
This question requires more information. In reference to what?
Thank you so much I love you man❤️❤️❤️❤️
Much love back! Thanks for watching and let me know if you ever have any questions!
COuld you please teach Degree distribution and power law
hi is it possible to help me with this question please? i ve been thinking about it for a week and i m blocked
Can you explain about automorphic graphs
Thanks for watching and the request! Do you mean graphs that have a non-trivial automorphism?
@@WrathofMath yes!
thank you! damn you talk through this like a boss!
My pleasure! So glad it helped!
@@WrathofMath Can you do a video on strong induction and non-homogenous recurrence relations? I love the way you explain everything. I have a really hard time understanding these two concepts.
you are the best!
A & B are isomorphic: 5 verts, all verts have 2 edges, both graphs have 5 Hamiltonian Circuits each with 5 steps.
C is not isomorphic to any because it has a vert with 4 edges while no other graph has a vert with 4 edges.
D is not isomorphic because it has 4 verts while all others have 5 verts.
very clear, thx
Glad to help!
Nice like always God bless you
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Isomorphic graphs? More like "Incredible knowledge that gets"...you good grades on tests!
Where are you from?
Easy to understand....
A and B are not isomorphic
- Same number of vertices
- Same number of edges
- Same sequence of vertex degrees
- Same edge connections (i.e., adjacency matrix)
But differing only in planarity (one is planar, and the other is non-planar)
Bijection is 1to1 unto correspondence
Yes it is!
THANK U SO MUCHHHH
here is the graph image
imgur.com/a/66nkvl7
Greate tut, thanks
My pleasure - glad to help!
Bro thank you that's all I can say 😭
Glad to help, thanks for watching!
The so called “isomorphic” in simple words is Invertible Linear Transformation.
A and B are isomorphic graphs
Graphs A and B are isomorphic but C and D are not.
Right on, good work!
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1 and 2 are isomorphic
Thank you
You're welcome! Thanks for watching!
nice, thanks
My pleasure!
you're af ucking legend
Thank you, I do my best!
A B are isomorphism, but CD not
Is this Demetri from Cobra Kai?
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thx
ο κολοκτρωνης με εφερε εδω
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