Geodesic
Sharp bounds for the number of matchings in generalized-theta-graphs
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 4, pp. 771-782.

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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 
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Dolati, Ardeshir; Golalizadeh, Somayyeh. Sharp bounds for the number of matchings in generalized-theta-graphs. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 4, pp. 771-782. http://geodesic.mathdoc.fr/item/DMGT_2012_32_4_a11/

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