Very intuitive explanation! Every other explanation I found was too formal and esoteric, devoid of any meaningful examples, but your video clarified it wonderfully! Thanks 👍
@VitalSine3 жыл бұрын
I'm happy to hear my video was helpful to you. Thanks for commenting :)
@mahaan6218 Жыл бұрын
This video taught me about the Cartesian product of graphs the best way 😍 Thank you sir!
@VitalSine Жыл бұрын
I'm glad it was helpful! 🙂
@golden_smaug11 ай бұрын
Books' definitions are usually quite cumbersome but thanks to this video I got a good grasp of what it is a cartesian product, thanks! :)
@atrsankaralingamvalarmathi33 жыл бұрын
Excellent explanation... Could you plz make some videos regarding algebraic graphs... thank you
@VitalSine3 жыл бұрын
Sure thing, I can make some videos on algebraic graph theory.
@atrsankaralingamvalarmathi33 жыл бұрын
@@VitalSine Thanks a lot Sir🙏
@rembautimes88083 жыл бұрын
Very well explained. Thanks a lot for taking the effort to make this topic clear
@VitalSine3 жыл бұрын
You're very welcome, happy to hear it was helpful :)
@monikaparmar20613 жыл бұрын
Came here from Reddit!
@VitalSine3 жыл бұрын
Welcome! Hope you like the video :)
@ashlyantony15073 жыл бұрын
Very helpful video. Thank you so much
@todianmishtaku6249 Жыл бұрын
Lovely explained!
@mahakaransandhu9173 жыл бұрын
Great video, very clear explanation, thank you!
@VitalSine3 жыл бұрын
You're very welcome, I'm glad you liked it 😀
@silviupavel69662 жыл бұрын
Thank you so much!!!
@MathwithWaqasShah2 жыл бұрын
great explanation sir. really helpful. you earned my subscription. thanks
@VitalSine2 жыл бұрын
Thank you!
@tomfogle8173 Жыл бұрын
Sick! Well done
@VitalSine Жыл бұрын
0:00 Review 1:05 Definition 3:15 Example 1 6:53 Example 2 8:51 Intuition
@PhilBoswell3 жыл бұрын
Nice video, but your outro is very loud compared to the rest, it comes as a nasty shock on headphones 🔊 I look forward to the next one.
@VitalSine3 жыл бұрын
Thanks for the feedback, I'm going to work on making it softer for my future videos. Glad you liked the video :)
@sharmilamuthukumar2383 жыл бұрын
Super
@VitalSine3 жыл бұрын
Thanks for watching! I'm glad you enjoyed the video :)
@rajeshkumarrout11923 жыл бұрын
great
@user-dp8gt2vh7k3 жыл бұрын
Hi teacher can you help me prove that G×Hisomorphism H×G
@VitalSine3 жыл бұрын
Hello and welcome to the channel! To start, you could label the vertices of the arbitrary graph G with u_1, u_2, ... u_m, and the vertices of the arbitrary graph H with v_1, v_2, ... v_n. Note that the vertex set of G x H = the cartesian product of vertex set of G and vertex set of H = vertex set of H x G. In other words, the vertex sets of both are the pairs (u_a, v_b) for all vertices u_a in G and all v_b in H. Now create a function f((u_a, v_b)) = (v_a, u_b) that will map vertices in G x H to vertices in H x G. First note that the function is a bijection between vertices of G x H and H x G. It also preserves adjacencies. Why? Suppose (u_a, v_b) and (u_c, v_d) are adjacent in G x H. Then either (u_a = u_c and v_b ~ v_d), or (v_b = v_d and u_a ~ u_c). Now apply our function to these vertices to get their respective vertices in H x G. f((u_a, v_b)) = (v_a, u_b) and f((u_c, v_d)) = (v_d, u_c). (v_a, u_b) ~ (v_d, u_c) because either (u_a = u_c and v_b ~ v_d), or (v_b = v_d and u_a ~ u_c), as we know one of these is true since we assumed the vertices (u_a, v_b) and (u_c, v_d) were adjacent in G x H. What we've just done is create a function that maps each vertex in G x H to one in H x G, preserving adjacencies between pairs of vertices, so G x H is isomorphic to H x G.
@user-dp8gt2vh7k3 жыл бұрын
@@VitalSine mirce sir ..thank you sooo much🌻🌻🌻
@VitalSine3 жыл бұрын
@Reham A_H Glad I could help 👍
@user-dp8gt2vh7k3 жыл бұрын
@@VitalSine 🌼🌼🌼🌼 l can communcate with you by telegram or masinger im study master but i am having difficulty to graph theory