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