Graph power

In graph theory, a branch of mathematics, the kth power G^k of an undirected graph G is another graph that has the same set of vertices, but in which two vertices are adjacent when their distance in G is at most k. Powers of graphs are referred to using terminology similar to that of exponentiation of numbers: G² is called the square of G, G³ is called the cube of G, etc.^[1]

Graph powers should be distinguished from the products of a graph with itself, which (unlike powers) generally have many more vertices than the original graph.