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Discussiones Mathematicae Graph Theory 32(4) (2012)
771-782
DOI: https://doi.org/10.7151/dmgt.1646
Sharp Bounds for the Number of Matchings in Generalized-theta-graphs
Ardeshir Dolati
Department of Mathematics & Computer Science | Somayyeh Golalizadeh
Young Researchers Club, Islamic Azad University |
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
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