Graph power

Summary

In graph theory, a branch of mathematics, the $k$th 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: $G^{2}$ is called the square of $G$, $G^{3}$ is called the cube of $G$, etc.