The expected values of the total numbers of independent edge sets and independent sets in random alpha-type pentagonal chains [PDF]
Heliyon, 2023 A independent edge set of G containing mutually independent edges is also called a matching of G. The total numbers of matchings and independent sets of a graph G, namely, the Hosoya index and the Merrifield-Simmons index, respectively, are two important
Lina Wei, Hong Bian, Haizheng Yu
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On Merrifield-Simmons index of molecular graphs [PDF]
Kragujevac Journal of Science, 2016 The Merrifield-Simmons index σ = σ(G) of a graph G is the number of independent vertex sets of G. This index can be calculated recursively and expressed in terms of Fibonacci numbers.
Gutman Ivan +2 more
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The Hosoya index and the Merrifield-Simmons index of some graphs [PDF]
Transactions on Combinatorics, 2012 The Hosoya index and the Merrifield-Simmons index are two types of graph invariants used in mathematical chemistry. In this paper, we give some formulas for computed these indices for some classes of corona product and link of two graphs. Furthermore, we
Samaneh Hossein-Zadeh +3 more
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The Hosoya index and the Merrifield–Simmons index [PDF]
Journal of Mathematical Chemistry, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Yufeng +2 more
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Graphs with maximal Hosoya index and minimal Merrifield–Simmons index
Discrete Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stephan Wagner, Zhongxun Zhu, Cao Yuan
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Merrifield-Simmons Index in Random Phenylene Chains and Random Hexagon Chains [PDF]
Discrete Dynamics in Nature and Society, 2015 The author obtains explicit expressions for the expected value of the Merrifield-Simmons index of a random phenylene chain and a random hexagon chain, respectively.
Ailian Chen
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On the Hosoya index and the Merrifield–Simmons index of graphs with a given clique number
Applied Mathematics Letters, 2010 Let \(C(n,k)\) be the class of all graphs of order \(n\) and the clique number \(k\). The author shows that in \(C(n,k)\) the Turan graph has the maximum number of matchings and the minimum number of independent sets. On other hand it is shown that the graph obtained from the complete graph \(G\) by adding new edges incident with a vertex of \(G\) has ...
Kexiang Xu
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The Merrifield-Simmons Index and Hosoya Index of C(n,k,λ) Graphs
Journal of Applied Mathematics, 2012 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 ...
Shaojun Dai, Ruihai Zhang
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The Expected Value of Hosoya Index and Merrifield–Simmons Index in a Random Cyclooctylene Chain
Axioms, 2022 The Hosoya index m(G) and the Merrifield–Simmons index i(G) of a graph G are the number of matchings and the number of independent sets in G. In this paper, we establish exact formulas for the expected value of the Hosoya index and Merrifield–Simmons ...
Yushuang Sun, Xianya Geng
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The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four
Journal of Mathematics, 2021 The Merrifield–Simmons index iG of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, i.e., the number of independent vertex sets of G.
Kun Zhao, Shangzhao Li, Shaojun Dai
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