How do Repeated Graph Powers Work? [Graph Theory Tutorial]

In this video, we'll examine the properties of repeated graph powers, such as the repeated square of a graph. We'll look at what happens to the distance between two vertices when we take the k-th power of a graph, and use this knowledge to prove the power rule of exponents for graph powers. That is, the rule that for any graph, G, (G^n)^m = G^(nm).

To recap, the k-th power of a graph G is an operation that copies its input graph, G, and then connects all pairs of vertices that were at most k apart in the input graph. The resulting graph is the k-th power of G.

If you enjoyed this video, I recommend you check out the other videos in my graph theory playlist:    • Graph Theory Tutorials