Tensor Product of Graphs Tutorial [Discrete Mathematics]

What is the tensor product of graphs? This video explains how to find the tensor product of two graphs and the definition of the graph tensor product. We'll cover examples of graph tensor products so that you build familiarity with this concept.
The tensor product of two undirected graphs G and H is denoted by G x H. The tensor product of 2 graphs G and H is a binary operation and produces a new graph with vertex set equal to the cartesian product of the vertex sets of graphs G and H, where two vertices in the tensor product are adjacent if their corresponding vertices in G are adjacent and their corresponding vertices in H are adjacent. I recommend you check out my videos on Cartesian products of graphs for some background information prior to watching this video.
If you want to learn more about graph products, I highly recommend the following book:
"Handbook of Product Graphs": amzn.to/3HjF5D8
Note: This is my Amazon Affiliate link. As an Amazon Associate I may earn commissions for purchases made through the link above, at no extra cost to you.
0:00 Definition
1:15 Tensor vs Cartesian product
1:27 Example 1
3:18 Example 2
5:55 Example 3
6:54 Intuition

[@todianmishtaku6249]

Lovely explained!

[@yusufturhan8367]

very interesting topic and great explanation!

[@johannes8144]

Thank you for your video! Nice explanation.

[@VitalSine]

You're very welcome 👍

[@VitalSine]

0:00 Definition 1:15 Tensor vs Cartesian product 1:27 Example 1 3:18 Example 2 5:55 Example 3 6:54 Intuition

[@VitalSine]

Hello everyone. I wanted to share this interesting link on a recently disproved conjecture relating to tensor products: en.wikipedia.org/wiki/Hedetniemi%27s_conjecture👍

[@rembautimes8808]

My Guess is that the tensor product of 2 disconnected graphs are disconnected . For 2 bipartite graps each vertice in the product set can only connect if they are adjacent in the factor graphs. So since only sets connect to other sets in the factor graph, they can’t connect to the same set in the product graph so it’s bipartite

[@VitalSine]

You're correct for both! For the first one, if either factor graph is disconnected, then the vertices with left/right entries in one connected component cannot connect to those with left/right entries in the other connected component, so the disconnected structure kind of carries over to the tensor product. And you're exactly right about the reason for why the tensor product of bipartite graphs is bipartite. 👍