What is the Cartesian Product of Graphs? (Discrete Math) +3 examples!

[@davideographer4410]

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 👍

[@VitalSine]

I'm happy to hear my video was helpful to you. Thanks for commenting :)

[@mahaan6218]

This video taught me about the Cartesian product of graphs the best way 😍 Thank you sir!

[@VitalSine]

I'm glad it was helpful! 🙂

[@golden_smaug]

Books' definitions are usually quite cumbersome but thanks to this video I got a good grasp of what it is a cartesian product, thanks! :)

[@atrsankaralingamvalarmathi3]

Excellent explanation... Could you plz make some videos regarding algebraic graphs... thank you

[@VitalSine]

Sure thing, I can make some videos on algebraic graph theory.

[@atrsankaralingamvalarmathi3]

@@VitalSine Thanks a lot Sir🙏

[@rembautimes8808]

Very well explained. Thanks a lot for taking the effort to make this topic clear

[@VitalSine]

You're very welcome, happy to hear it was helpful :)

[@monikaparmar2061]

Came here from Reddit!

[@VitalSine]

Welcome! Hope you like the video :)

[@ashlyantony1507]

Very helpful video. Thank you so much

[@todianmishtaku6249]

Lovely explained!

[@mahakaransandhu917]

Great video, very clear explanation, thank you!

[@VitalSine]

You're very welcome, I'm glad you liked it 😀

[@silviupavel6966]

Thank you so much!!!

[@MathwithWaqasShah]

great explanation sir. really helpful. you earned my subscription. thanks

[@VitalSine]

Thank you!

[@tomfogle8173]

Sick! Well done

[@VitalSine]

0:00 Review 1:05 Definition 3:15 Example 1 6:53 Example 2 8:51 Intuition

[@PhilBoswell]

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.

[@VitalSine]

Thanks for the feedback, I'm going to work on making it softer for my future videos. Glad you liked the video :)

[@sharmilamuthukumar238]

Super

[@VitalSine]

Thanks for watching! I'm glad you enjoyed the video :)

[@rajeshkumarrout1192]

great

[@user-dp8gt2vh7k]

Hi teacher can you help me prove that G×Hisomorphism H×G

[@VitalSine]

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-dp8gt2vh7k]

@@VitalSine mirce sir ..thank you sooo much🌻🌻🌻

[@VitalSine]

@Reham A_H Glad I could help 👍

[@user-dp8gt2vh7k]

@@VitalSine 🌼🌼🌼🌼 l can communcate with you by telegram or masinger im study master but i am having difficulty to graph theory