Note: On the matching polynomial of subdivision graphs

Authors:
Weigen Yan;Yeong-Nan Yeh
Affiliations:
School of Sciences, Jimei University, Xiamen 361021, China;Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan
Venue:
Discrete Applied Mathematics
Year:
2009

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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.