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.

Some fun facts about tensor products: -Graphs that can be represented as tensor products are connected only if both its factor graphs are connected and at least one is nonbipartite. -The tensor product of two complete graphs is the complement of a rook's graph

If you liked this video, I recommend you check out my graph theory playlist: https://www.youtube.com/playlist?list=PLZ2xtht8y2-Jx8hxFvnFQfEej1PzqFbVX

Here are some links for further exploration of graph tensor products: https://en.wikipedia.org/wiki/Tensor_product_of_graphs https://mathworld.wolfram.com/GraphCategoricalProduct.html https://mathworld.wolfram.com/BipartiteDoubleGraph.html https://en.wikipedia.org/wiki/Graph_product

Discord: https://discord.gg/dvpXxBy ... https://www.youtube.com/watch?v=JeB96BLaMTY