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

This video will explain what a cartesian product in graph theory is and how to calculate it.

The Cartesian product of 2 graphs, G and H, is itself a graph with vertex set equal to the cartesian product of the vertex sets of graphs G and H, with order equal to the product of the orders of graphs G and H, and adjacencies between vertices defined as follows: two vertices (u,u' ) and (v,v' ) are adjacent in G * H if and only if either u = v and u' is adjacent to v' in H, or u' = v' and u is adjacent to v in G.

The Cartesian product of 2 graphs is just one of many graph products, which are operations on graphs that create new graphs from factor graphs.

By learning about graph products, we can change our perspective on what graphs are. Just like numbers multiply and divide, in addition to representing a constant quantity, graphs, too, can act upon each other through graph products. This video gives you a visual perspective on the cartesian product of 2 graphs and walks you through several examples so you know how to calculate this product yourself for any two graphs.

Thanks for watching!

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00:00 Review
01:05 Definition
03:15 Example 1
06:53 Example 2
08:51 Intuition