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On coefficients of circuit polynomials and characteristic polynomials. (English) Zbl 0596.05005

Author’s abstract: ”Results are given from which expressions for the coefficients of the simple circuit polynomial of a graph can be obtained in terms of subgraphs of the graph. From these are deduced parallel results for the coefficients of the characteristic polynomial of a graph. Some specific results are presented on the parities of the coefficients of characteristic polynomials. A characterization is then determined for graphs in which the number of sets of independent edges is always even. This leads to an interesting link between matching polynomials and characteristic polynomials. Finally explicit formulae are derived for the number of ways of covering two well-known families of graphs with node disjoint circuits, and for the first few coefficients of their characteristic polynomials.”
Reviewer: I.Strazdins

MSC:

05A15 Exact enumeration problems, generating functions
05C38 Paths and cycles
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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