TAILIEUCHUNG - Báo cáo toán học: "Sharp lower bound for the total number of matchings of tricyclic graphs"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài:Sharp lower bound for the total number of matchings of tricyclic graphs. | Sharp lower bound for the total number of matchings of tricyclic graphs Shuchao Li Zhongxun Zhu Faculty of Mathematics and Statistics Central China Normal University Wuhan 430079 . China lscmath@ Faculty of Mathematics and Statistics South Central University for Nationalities Wuhan 430074 . China zzxun73@ Submitted Mar 26 2010 Accepted Aug 24 2010 Published Oct 5 2010 Mathematics Subject Classifications 05C69 05C35 Abstract Let Tn be the class of tricyclic graphs on n vertices. In this paper a sharp lower bound for the total number of matchings of graphs in Tn is determined. 1 Introduction The total number of matchings of a graph is a graphic invariant which is important in structural chemistry. In the chemistry literature this graphic invariant is called the Hosoya index of a molecular graph. It was applied to correlations with boiling points entropies calculated bond orders as well as for coding of chemical structures 12 13 26 32 . Therefore the ordering of molecular graphs in terms of their Hosoya indices is of interest in chemical thermodynamics. Let G be a graph with n vertices and m G k the number of its k-matchings. It is convenient to denote m G 0 1 and m G k 0 for k n 2 . The Hosoya index of G denoted by z G is defined as the sum of all the numbers of its matchings namely n 2 z G m G k . k 0 The Hosoya index was introduced by Hosoya 13 and since then many researchers have investigated this graphic invariant . see 2 4 5 12 . An important direction Financially supported by self-determined research funds of CCNU from the colleges basic research and operation of MOE CCNU09Y01005 CCNU09Y01018 and the National Science Foundation of China Grant No. 11071096 . THE ELECTRONIC JOURNAL OF COMBINATORICS 17 2010 R132 1 is to determine the graphs with maximal or minimal Hosoya indices in a given class of graphs. As for n-vertex trees it has been shown that the path has the maximal Hosoya index and the star has the minimal Hosoya index see

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