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• W2990930757 abstract "Let k ≥ 1 and q1,..., qk be some positive integers. The generalized theta graph q1,...,qk is the graph that is formed by taking a pair of vertices u and v, and joining them by k internally disjoint paths of lengths q1,..., qk. Let CC be the graph that obtained by attaching some cycles to at most two vertices with degree k of the generalized theta graph q1,...,qk. An edge covering of a graph is a set of edges such that every vertex of the graph is incident to at least one edge of the set. Let G be a simple graph with m edges. The edge cover polynomial of G is the polynomial E(G,x) = Σm i=1 e(G,i)xi, where e(G,i) is the number of edge coverings of G of size i. Let t be a positive integer and Ft be the friendship (or Dutch windmill) graph with 2t + 1 vertices and 3t edges. In this paper we obtain the number of perfect matchings of CC graphs and then study the edge cover polynomial of friendship graphs. We show that the friendship graphs are determined by their edge cover polynomials. We find that all non-zero roots of the edge cover polynomial of friendship graphs are simple. Finally we prove that the edge cover polynomials of friendship graphs are unimodal." @default.
• W2990930757 created "2019-12-05" @default.
• W2990930757 creator A5015969326 @default.
• W2990930757 date "2019-01-01" @default.
• W2990930757 modified "2023-09-24" @default.
• W2990930757 title "On the number of perfect matchings of generalized theta graphs and the edge cover polynomials of friendship graphs" @default.
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• W2990930757 doi "https://doi.org/10.2298/fil1901111o" @default.
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