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Sharp bounds for the number of matchings in generalized-theta-graphs

Ardeshir DolatiSomayyeh Golalizadeh — 2012

Discussiones Mathematicae Graph Theory

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.

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