Discussiones Mathematicae Graph Theory 32(4) (2012) 771-782
doi: 10.7151/dmgt.1646

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Sharp Bounds for the Number of Matchings in Generalized-theta-graphs

Ardeshir Dolati

Department of Mathematics & Computer Science
Shahed University, Tehran, PO Box: 18151-159, Iran

Somayyeh Golalizadeh

Young Researchers Club, Islamic Azad University
Ardabil branch, Ardabil, Iran

Abstract

A generalized-theta-graph is a graph consisting of a pair of end vertices joined by k (k ≥ 3) internally disjoint paths. We denote the family of all the n-vertex generalized-theta-graphs with k paths between end vertices by Θnk. In this paper, we determine the sharp lower bound and the sharp upper bound for the total number of matchings of generalized-theta-graphs in Θnk. In addition, we characterize the graphs in this class of graphs with respect to the mentioned bounds.

Keywords: generalized-theta-graph, matching, Fibonacci number, Hosoya index

2010 Mathematics Subject Classification: 05C30, 05C70, 05C75.

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Received 12 August 2011
Revised 25 January 2012
Accepted 30 January 2012