On the Merrifield–Simmons index of tricyclic graphs

Kinkar Chandra Das; Suresh Elumalai; Surojit Ghosh; Toufik Mansour

doi:10.1016/j.dam.2022.09.006

On the Merrifield–Simmons index of tricyclic graphs

Kinkar Chandra Das
, Suresh Elumalai
, Surojit Ghosh
, Toufik Mansour

Department of Mathematics

SRM Institute of Science and Technology
Indian Institute of Technology Roorkee
University of Haifa

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

6 Scopus citations

Abstract

The total number of independent subsets, including the empty set, of a graph, is also termed as the Merrifield–Simmons index (MSI) in mathematical chemistry. Zhu and Yu (2012) presented a lower bound on Merrifield–Simmons index of tricyclic graphs in terms of order n and the characterization of extremal graphs. This result was erroneous. In this paper, we correct this result. Moreover, we characterize the tricyclic graphs on n vertices with the second and third smallest values of the Merrifield–Simmons index.

Original language	English
Pages (from-to)	342-354
Number of pages	13
Journal	Discrete Applied Mathematics
Volume	322
DOIs	https://doi.org/10.1016/j.dam.2022.09.006
State	Published - 15 Dec 2022

Keywords

Fibonacci number
Independent set
Merrifield–Simmons index
Tricyclic graph

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10.1016/j.dam.2022.09.006

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title = "On the Merrifield–Simmons index of tricyclic graphs",

abstract = "The total number of independent subsets, including the empty set, of a graph, is also termed as the Merrifield–Simmons index (MSI) in mathematical chemistry. Zhu and Yu (2012) presented a lower bound on Merrifield–Simmons index of tricyclic graphs in terms of order n and the characterization of extremal graphs. This result was erroneous. In this paper, we correct this result. Moreover, we characterize the tricyclic graphs on n vertices with the second and third smallest values of the Merrifield–Simmons index.",

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doi = "10.1016/j.dam.2022.09.006",

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T1 - On the Merrifield–Simmons index of tricyclic graphs

AU - Das, Kinkar Chandra

AU - Elumalai, Suresh

AU - Ghosh, Surojit

AU - Mansour, Toufik

PY - 2022/12/15

Y1 - 2022/12/15

N2 - The total number of independent subsets, including the empty set, of a graph, is also termed as the Merrifield–Simmons index (MSI) in mathematical chemistry. Zhu and Yu (2012) presented a lower bound on Merrifield–Simmons index of tricyclic graphs in terms of order n and the characterization of extremal graphs. This result was erroneous. In this paper, we correct this result. Moreover, we characterize the tricyclic graphs on n vertices with the second and third smallest values of the Merrifield–Simmons index.

AB - The total number of independent subsets, including the empty set, of a graph, is also termed as the Merrifield–Simmons index (MSI) in mathematical chemistry. Zhu and Yu (2012) presented a lower bound on Merrifield–Simmons index of tricyclic graphs in terms of order n and the characterization of extremal graphs. This result was erroneous. In this paper, we correct this result. Moreover, we characterize the tricyclic graphs on n vertices with the second and third smallest values of the Merrifield–Simmons index.

KW - Fibonacci number

KW - Independent set

KW - Merrifield–Simmons index

KW - Tricyclic graph

UR - https://www.scopus.com/pages/publications/85138379532

U2 - 10.1016/j.dam.2022.09.006

DO - 10.1016/j.dam.2022.09.006

M3 - Article

AN - SCOPUS:85138379532

SN - 0166-218X

VL - 322

SP - 342

EP - 354

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

On the Merrifield–Simmons index of tricyclic graphs

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Keywords

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