Comparison between Merrifield-Simmons Index and Wiener Index of Graphs

Ke Xiang Xu; Kinkar Chandra Das; Ivan Gutman; Meng Lu Wang

doi:10.1007/s10114-022-0540-9

Comparison between Merrifield-Simmons Index and Wiener Index of Graphs

Ke Xiang Xu
, Kinkar Chandra Das
, Ivan Gutman
, Meng Lu Wang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

The Merrifield-Simmons index σ is the total number of independent vertex sets (including the empty set) of the graph G. The Wiener index W is the sum of distances in all unordered pairs of vertices of G. We construct some new graphs satisfying σ > W and W > σ, respectively. In particular, infinite graphs satisfying W > σ are invented with graphs with diameter 2 and infinite ones satisfying σ > W are discovered with so-called universally diametrical graphs.

Original language	English
Pages (from-to)	2220-2230
Number of pages	11
Journal	Acta Mathematica Sinica, English Series
Volume	38
Issue number	12
DOIs	https://doi.org/10.1007/s10114-022-0540-9
State	Published - Dec 2022

Keywords

05C07
05C70
Cartesian product
Fibonacci number
independence number
Merrifield-Simmons index
universally diametrical graph
Wiener index

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10.1007/s10114-022-0540-9

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title = "Comparison between Merrifield-Simmons Index and Wiener Index of Graphs",

abstract = "The Merrifield-Simmons index σ is the total number of independent vertex sets (including the empty set) of the graph G. The Wiener index W is the sum of distances in all unordered pairs of vertices of G. We construct some new graphs satisfying σ > W and W > σ, respectively. In particular, infinite graphs satisfying W > σ are invented with graphs with diameter 2 and infinite ones satisfying σ > W are discovered with so-called universally diametrical graphs.",

keywords = "05C07, 05C70, Cartesian product, Fibonacci number, independence number, Merrifield-Simmons index, universally diametrical graph, Wiener index",

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T1 - Comparison between Merrifield-Simmons Index and Wiener Index of Graphs

AU - Xu, Ke Xiang

AU - Das, Kinkar Chandra

AU - Gutman, Ivan

AU - Wang, Meng Lu

PY - 2022/12

Y1 - 2022/12

N2 - The Merrifield-Simmons index σ is the total number of independent vertex sets (including the empty set) of the graph G. The Wiener index W is the sum of distances in all unordered pairs of vertices of G. We construct some new graphs satisfying σ > W and W > σ, respectively. In particular, infinite graphs satisfying W > σ are invented with graphs with diameter 2 and infinite ones satisfying σ > W are discovered with so-called universally diametrical graphs.

AB - The Merrifield-Simmons index σ is the total number of independent vertex sets (including the empty set) of the graph G. The Wiener index W is the sum of distances in all unordered pairs of vertices of G. We construct some new graphs satisfying σ > W and W > σ, respectively. In particular, infinite graphs satisfying W > σ are invented with graphs with diameter 2 and infinite ones satisfying σ > W are discovered with so-called universally diametrical graphs.

KW - 05C07

KW - 05C70

KW - Cartesian product

KW - Fibonacci number

KW - independence number

KW - Merrifield-Simmons index

KW - universally diametrical graph

KW - Wiener index

UR - https://www.scopus.com/pages/publications/85134300302

U2 - 10.1007/s10114-022-0540-9

DO - 10.1007/s10114-022-0540-9

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EP - 2230

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 12

ER -

Comparison between Merrifield-Simmons Index and Wiener Index of Graphs

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Keywords

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