Chemical graph theory by Danail Bonchev; Dennis H Rouvray

By Danail Bonchev; Dennis H Rouvray

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For intermediate values of m, n � 1 < m < (n — l)(n — 2)/2, another concept to establish the connectedness of a graph is needed; such a concept is that of the spanning tree of a graph outlined below. Let G he a connected graph with n vertices and m = n � 1 edges. G contains no cyde because the necessary edge is not available for the closure of an open path wra E G into a cycle. Connected graphs without cydes are called trees, and usually denoted by the symbol T. The number of vertices n and edges m of a tree are related by the condition «m�*.

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