Saw that you responded to a comment from 3 weeks ago on a video posted 4 years ago, that is some serious dedication. I'm planning on watching the rest of this series 5 episodes a day to try and keep up with the graph theory group in my research program. I'm working on some probability and neural networks stuff so their research really isn't related to mine lol but I'm still interested in this stuff for general mathematical knowledge! Are there any common textbooks used for graph theory?
Thank you! For the longest time, this playlist was completely unsorted. Since then, I have made a lot of progress sorting it, however there are still videos which are out of order, so be aware of that. There are also certainly still lots of holes I still intend to fill in!
Glad to help! Thanks for watching and check out my graph theory playlist if you're looking for more! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
My answers to the questions in the description box are these are they right? Yes the order can be equal to the size for example in the case of a triangle there are three edges and three vertices But no the size can't be greater than the order because the size is the cardinality of edges and edges are joining two vertices so the number of edges can't be greater than the number of vertices. And thank you so much
Thanks for watching and for the question! The cardinality of a set is the number of elements in the set, when we talk about graphs we call the cardinality of the vertex set the order and the cardinality of the edge set the size. However, the cardinality of a set S is written |S|, and sometimes, if G is a graph, |G| is written to mean the order of G, as in the cardinality of the vertex set, which is the number of vertices in G.
Thanks for watching and I am not sure what you mean. The order of a graph is its number of vertices, and the size of a graph is its number of edges. So, in a finite graph, to measure its order or size we just counts its number of vertices or edges. Of course, for certain graphs, we may employ different counting techniques to determine these numbers. For example, how many edges are in a complete bipartite graph with 4 vertices in one partite set, and 3 vertices in the other? Well, by definition of such a graph, each of the 4 vertices in one set are adjacent to all 3 of the vertices in the other set, so the number of edges in 4*3 = 12.
Better explained than every one of my professors, thanks for your concise explanations
You're very welcome, I am glad it helped and thanks for watching!
Saw that you responded to a comment from 3 weeks ago on a video posted 4 years ago, that is some serious dedication. I'm planning on watching the rest of this series 5 episodes a day to try and keep up with the graph theory group in my research program. I'm working on some probability and neural networks stuff so their research really isn't related to mine lol but I'm still interested in this stuff for general mathematical knowledge! Are there any common textbooks used for graph theory?
This review is a really good add in the order of videos. Especially seeing how I'm watching the videos chronologically
Thank you! For the longest time, this playlist was completely unsorted. Since then, I have made a lot of progress sorting it, however there are still videos which are out of order, so be aware of that. There are also certainly still lots of holes I still intend to fill in!
@@WrathofMath can you learn out of order?
As you can see the SIZE is ended with E (then E= Edges), that is quite easy to memory.
Thanks for pointing that out!
Awesome! thanks for an excellent explanation.
size backwards is ezis, which sounds like edges.
Wow, that's a super ezi way to remember things!
A great help for me. thank u sir😊
My pleasure, thanks for watching!
thanks for that
Glad to help - thanks for watching!
Fantastic ❤❤
Thank you!
Great! Really, helpful
Thanks for watching and I'm glad it helped :)
you are amazing, thanks for that
Glad to help! Thanks for watching and check out my graph theory playlist if you're looking for more! th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
My answers to the questions in the description box are these are they right?
Yes the order can be equal to the size for example in the case of a triangle there are three edges and three vertices
But no the size can't be greater than the order because the size is the cardinality of edges and edges are joining two vertices so the number of edges can't be greater than the number of vertices.
And thank you so much
Nice.... helped lot.....
Glad to hear it and thank you for watching. Let me know if you ever have any lesson requests for the channel!
Order and size? More like "Wonderful lectures before my eyes!" 👀
What is exactly the cardinality , is it number of edges or vertices ?
Thanks for watching and for the question! The cardinality of a set is the number of elements in the set, when we talk about graphs we call the cardinality of the vertex set the order and the cardinality of the edge set the size. However, the cardinality of a set S is written |S|, and sometimes, if G is a graph, |G| is written to mean the order of G, as in the cardinality of the vertex set, which is the number of vertices in G.
@@WrathofMath great thanks you
Helpful
Thanks for watching and I am glad you found it helpful!
🎉🎉🎉
thanks
You're welcome, thanks for watching!
How can we measure "order of graph" and "size of graph" please sir kindly answer tell me
Thanks for watching and I am not sure what you mean. The order of a graph is its number of vertices, and the size of a graph is its number of edges. So, in a finite graph, to measure its order or size we just counts its number of vertices or edges. Of course, for certain graphs, we may employ different counting techniques to determine these numbers. For example, how many edges are in a complete bipartite graph with 4 vertices in one partite set, and 3 vertices in the other? Well, by definition of such a graph, each of the 4 vertices in one set are adjacent to all 3 of the vertices in the other set, so the number of edges in 4*3 = 12.
@@WrathofMath Thank you sir