Article ID Journal Published Year Pages File Type
419802 Discrete Applied Mathematics 2009 6 Pages PDF
Abstract

Let GG be a simple graph and let S(G)S(G) be the subdivision graph of GG, which is obtained from GG by replacing each edge of GG by a path of length two. In this paper, by the Principle of Inclusion and Exclusion we express the matching polynomial and Hosoya index of S(G)S(G) in terms of the matchings of GG. Particularly, if GG is a regular graph or a semi-regular bipartite graph, then the closed formulae of the matching polynomial and Hosoya index of S(G)S(G) are obtained. As an application, we prove a combinatorial identity.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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