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Graph power
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<p>In <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a>, a branch of mathematics, the kth power Gk of an <a href="/facts/Undirected_graph/kw3eIBUe">undirected graph</a> G is another graph that has the same set of <a href="/facts/Vertex_(graph_theory)/WhlWmL3o">vertices</a>, but in which two vertices are adjacent when their <a href="/facts/Distance_(graph_theory)/EmQFKvqa">distance</a> in G is at most k. Powers of graphs are referred to using terminology similar to that of <a href="/facts/Exponentiation/pac6QY2g">exponentiation</a> of numbers: <i>G</i>2 is called the <i><a href="/facts/Square_number/jfakASPK">square</a></i> of G, <i>G</i>3 is called the <i><a href="/facts/Cube_(algebra)/SqmlEEog">cube</a></i> of G, etc. </p><p>Graph powers should be distinguished from the <a href="/facts/Graph_product/ru7rPMFW">products</a> of a graph with itself, which (unlike powers) generally have many more vertices than the original graph. </p>