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

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

Cite this

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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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AU - Elumalai, Suresh

AU - Ghosh, Arpita

AU - Mansour, Toufik

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KW - Diameter

KW - Eccentric complexity

KW - Graph

KW - Independence number

KW - Merrifield–Simmons index

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JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

On conjecture of Merrifield–Simmons index

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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