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The Merrifield–Simmons index in (n, n + 1)-graphs

Journal of Mathematical Chemistry, 2006
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Hanyuan Deng, Shubo Chen
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Comparison between Merrifield-Simmons Index and Wiener Index of Graphs

Acta Mathematica Sinica, English Series, 2022
In a graph \(G=(V,E)\), the Merrifield-Simmons index of \(G\), \(\sigma(G)\), is the total number of independent sets (including the empty set) in \(G\). The Wiener index of \(G\) is defined as \(W(G)= \sum_{\{u,v\} \subseteq V}d_G(u,v)\). It is known that these two invariants are not comparable, i.e.\ there exist graphs \(G\) with \(\sigma(G) < W(G)\)
Xu, Kexiang, das, kinkar, Gutman, Ivan, Wang M.   +3 more
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On the Merrifield–Simmons index of tricyclic graphs

Discrete Applied Mathematics, 2022
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Suresh Elumalai, Toufik Mansour, Kinkar Chandra Das   +2 more
exaly   +2 more sources

On conjecture of Merrifield–Simmons index

Discrete Applied Mathematics, 2021
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Suresh Elumalai, Toufik Mansour, Kinkar Chandra Das   +2 more
exaly   +4 more sources

Unicycle graphs with extremal Merrifield–Simmons Index

Journal of Mathematical Chemistry, 2006
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Hongbo Hua
exaly   +3 more sources

Orderings of a class of trees with respect to the Merrifield–Simmons index and the Hosoya index

Journal of Combinatorial Optimization, 2019
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Xuesong Mei, Zheng Sun, Fei Zhao
exaly   +3 more sources

Maxima and Minima of the Hosoya Index and the Merrifield-Simmons Index

Acta Applicandae Mathematicae, 2010
The Hosoya index and the Merrifield-Simmons index are typical examples of graph invariants used in mathematical chemistry for quantifying relevant details of molecular structure. In recent years, quite a lot of work has been done on the extremal problem for these two indices, i.e., the problem of determining the graphs within certain prescribed classes
Wagner, Stephan, Gutman, Ivan
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Further results on the Merrifield–Simmons index

Discrete Applied Mathematics, 2020
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Hongbo Hua, Xinying Hua, Hongzhuan Wang
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