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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 for 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.
==Properties==
If a graph has diameter ''d'', then its ''d''-th power is the complete graph.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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