Abstract
Let G be a graph. With every connected subgraph of G, let us associate a weight (Wα and with every spanning subgrapha or cover) C of G, a weightwhere αi (i = 1, 2, …, n) are the components of C. The subgraph polynomial of G iswhere the summation is taken over all the spanning subgraphs in G.The basic properties of subgraph polynomials are given, expressions for the subgraph polynomials of multigraphs and pseudographs are derived, and the chromatic and dichromatic polynomials are shown to be special cases of the subgraph polynomial.
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