Graphs with given number of cut vertices and extremal Merrifield-Simmons index

Authors:
Hongbo Hua;Shenggui Zhang
Affiliations:
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, PR China and Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai'an, Jiangsu ...;Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, PR China
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

The Merrifield-Simmons index of a graph is defined as the total number of its independent sets, including the empty set. Denote by G(n,k) the set of connected graphs with n vertices and k cut vertices. In this paper, we characterize the graphs with the maximum and minimum Merrifield-Simmons index, respectively, among all graphs in G(n,k) for all possible k values.