What is the Complement of a Graph? | Graph Theory, Graph Complements, Self Complementary Graphs
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- เผยแพร่เมื่อ 26 ส.ค. 2024
- What is the complement of a graph? What are self complementary graphs? We'll be answering these questions in today's video graph theory lesson!
If G is a graph, the complement of G has the same vertex set but the "opposite" edge set. That means two vertices are adjacent in G Complement if and only if they are not adjacent in G. So where there is an edge in G, there is not an edge in G complement. Where there is not an edge in G, there is an edge in G complement.
If a graph is isomorphic to its complement, we say that graph is self complementary. Pretty cool!
In the lesson we go over the fact that if a graph is disconnected then its complement is connected. The converse of this statement is not true. If a graph is connected, its complement is not necessarily disconnected. Consider the path graph on 4 vertices.
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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It was very helpful. My graph theory course exam will start tomorrow morning and I was having problems in understanding some topics. Then you explained it very nicely. Thanks a lot.
How'd the exam go?
Complement of a graph? More like "Cool videos, with a knowledge-impartation ability that lasts!" 👍
Hello! Thanks for the great video! To answer the question you stated: n the explanation: if G is a connected graph,. its complement will be disconnected.
The last property was pretty awesome and just a surprise.
Great video, clear explanation. Really helped. Thank you!
Glad to hear it! Thanks a lot for watching and let me know if you ever have any video requests!
Man thks!!! And not only figurative I already sent you a little apreciation of my own 😉😉😉 i am self studying graphs and is a struggle with the dry concepts but with your explanations is smoother.thks again!!!🌟🌟🌟
I would be interested in seeing a video/explanation of how to find the number of ways a graph G can be properly colored with t colors. Like finding the equation p(G, t). Like for P_3 (path on 3 vertices), p(G, t) = t(t - 1)(t - 2) I believe. What about other graphs like C_4 (cycle on 4 vert.), C_5, or C_n? Or what about finding K_n (complete graphs on n vertices)?
Thanks for watching Parker, and for your request! That would be a lot of fun, I'll add it to my list of lessons to get to! I'm a bit behind on requests right now, but I'll get to them all in due time!
Thanks a lot
Your teaching method is really Awesome
Thank you!
¡Gracias!
Thanks so much, Calito! I just enabled the super thanks feature this week, you are the inaugural super thanker! 😊 I really appreciate it, and you've probably noticed I have a big graph theory playlist with over 150 videos - I hope they'll continue to be helpful. Let me know if you have any requests, and good luck with the self studying, I self studied graph theory too!
5:10 Is H complement a complete graph? Because it's missing two edges to get it to complete. Right?
Sir , How I can prove that the diameter of a self complementary is greater than or equal to 3 ??
Thank you very much Sir❤️ really helped me.
Glad to hear it, thanks for watching - and let me know if you ever have any questions! If you're looking for more graph theory, check out my playlist: th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
Great explanation
Thanks
Thank you! If you're looking for more graph theory, check out my graph theory playlist: th-cam.com/play/PLztBpqftvzxXBhbYxoaZJmnZF6AUQr1mH.html
thanks sir
What software are you using in this vid?
Yes it is
Thanks for watching! Yes what is what?
@@WrathofMath connected graph will become non-connected after complementary, that question was at the end of the video 😅
Such an awesome video, thank you so much for making content like this!
Thanks so much and it is my pleasure! Let me know if you ever have any lesson requests!
Anyone can say if the converse true or not?
converse is not true, i have found a counter example. Graph on 4 vertices which look like this X| , take its complement, its still connected.
So, the complement of a complete graph is a set of vertices with an empty set of edges.
you sound like bill gates
Thanks for watching! And you think so? I have not heard that comparison before, but I will take it as a complement! He's a good speaker!
saved me 🫶💜