Graph power

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.

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.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.