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

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

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

Bibliographical note

Publisher Copyright:
© 2022 Elsevier B.V.

Keywords

Fibonacci number
Independent set
Merrifield–Simmons index
Tricyclic graph

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.1016/j.dam.2022.09.006

Cite this

@article{38442243ca184d42b938bd68b3043cec,

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.",

keywords = "Fibonacci number, Independent set, Merrifield–Simmons index, Tricyclic graph",

author = "Das, {Kinkar Chandra} and Suresh Elumalai and Surojit Ghosh and Toufik Mansour",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2022",

month = dec,

day = "15",

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

language = "English",

volume = "322",

pages = "342--354",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier",

}

TY - JOUR

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 - http://www.scopus.com/inward/record.url?scp=85138379532&partnerID=8YFLogxK

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this