On conjecture of Merrifield–Simmons index

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

doi:10.1016/j.dam.2020.09.004

On conjecture of Merrifield–Simmons index

Kinkar Chandra Das, Suresh Elumalai, Arpita 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. The eccentric complexity of a graph G is defined to be the number of different eccentricities of its vertices. Hua et al. (2020) mentioned two open problems and a conjecture on the Merrifield–Simmons index and eccentric complexity of graph. In this paper we solve both open problems and a conjecture. Moreover, we generalize some of the results.

Original language	English
Pages (from-to)	211-217
Number of pages	7
Journal	Discrete Applied Mathematics
Volume	288
DOIs	https://doi.org/10.1016/j.dam.2020.09.004
State	Published - 15 Jan 2021

Bibliographical note

Funding Information:
The authors are much grateful to three anonymous referees for their valuable comments on our paper, which have considerably improved the presentation of this paper. S. Elumalai is supported by University of Haifa , Israel for the Postdoctoral studies. A. Ghosh is grateful to the University of Haifa for her position as adjunct researcher.

Funding Information:
The authors are much grateful to three anonymous referees for their valuable comments on our paper, which have considerably improved the presentation of this paper. S. Elumalai is supported by University of Haifa, Israel for the Postdoctoral studies. A. Ghosh is grateful to the University of Haifa for her position as adjunct researcher.

Publisher Copyright:
© 2020 Elsevier B.V.

Keywords

Diameter
Eccentric complexity
Graph
Independence number
Merrifield–Simmons index

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2020.09.004

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title = "On conjecture of Merrifield–Simmons index",

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. The eccentric complexity of a graph G is defined to be the number of different eccentricities of its vertices. Hua et al. (2020) mentioned two open problems and a conjecture on the Merrifield–Simmons index and eccentric complexity of graph. In this paper we solve both open problems and a conjecture. Moreover, we generalize some of the results.",

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N1 - Funding Information: The authors are much grateful to three anonymous referees for their valuable comments on our paper, which have considerably improved the presentation of this paper. S. Elumalai is supported by University of Haifa , Israel for the Postdoctoral studies. A. Ghosh is grateful to the University of Haifa for her position as adjunct researcher. Funding Information: The authors are much grateful to three anonymous referees for their valuable comments on our paper, which have considerably improved the presentation of this paper. S. Elumalai is supported by University of Haifa, Israel for the Postdoctoral studies. A. Ghosh is grateful to the University of Haifa for her position as adjunct researcher. Publisher Copyright: © 2020 Elsevier B.V.

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ER -

On conjecture of Merrifield–Simmons index

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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