The Merrifield-Simmons index and Hosoya index of \(C(n, k, \lambda)\) graphs
type: Item
instance of: scholarly article
title: The Merrifield-Simmons index and Hosoya index of \(C(n, k, \lambda)\) graphs
zbMATH Open document ID: 1255.05133
DOI: 10.1155/2012/520156
author: Shaojun Dai
author: Ruihai Zhang
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: The Merrifield-Simmons index \(i(G)\) of a graph \(G\) is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, that is, the number of independent vertex sets of \(G\). The Hosoya index \(z(G)\) of a graph \(G\) is defined as the total number of independent edge subsets, that is, the total number of its matchings. By \(C(n,k,\lambda)\) we denote the set of graphs with \(n\) vertices, \(k\) cycles, the length of every cycle is \(\lambda\), and all the edges not on the cycles are pendant edges which are attached to the same vertex. In this paper, we investigate the Merrifield-Simmons index \(i(G)\) and the Hosoya index \(z(G)\) for a graph \(G\) in \(C(n,k,\lambda)\).
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 6106237
zbMATH Keywords: Merrifield-Simmons index
zbMATH Keywords: number of independent vertex sets
zbMATH Keywords: Hosoya index
zbMATH Keywords: number of matchings
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/520156
OpenAlex ID: W1504126827
Wikidata QID: Q58906054
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DBLP publication ID: journals/jam/DaiZ12
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description: scientific article; zbMATH DE number 6106237