Elsevier

Discrete Mathematics

Volume 329, 28 August 2014, Pages 77-87
Discrete Mathematics

Graphs with maximal Hosoya index and minimal Merrifield–Simmons index

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Abstract

For a graph G, the Hosoya index and the Merrifield–Simmons index are defined as the total number of its matchings and the total number of its independent sets, respectively. In this paper, we characterize the structure of those graphs that minimize the Merrifield–Simmons index and those that maximize the Hosoya index in two classes of simple connected graphs with n vertices: graphs with fixed matching number and graphs with fixed connectivity.

Keywords

Matching number
Vertex connectivity
Merrifield–Simmons index
Hosoya index

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This project was supported by the Special Fund for Basic Scientific Research of Central Colleges, South-Central University for Nationalities (CZZ13006). The fourth author was supported by the National Research Foundation of South Africa, grant number 70560.