Maximum atom-bond connectivity index with given graph parameters

Xiu Mei Zhang; Yu Yang; Hua Wang; Xiao Dong Zhang

doi:10.1016/j.dam.2016.06.021

Maximum atom-bond connectivity index with given graph parameters

Xiu Mei Zhang, Yu Yang, Hua Wang, Xiao Dong Zhang

Mathematical Sciences

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

23 Scopus citations

Abstract

The atom-bond connectivity (ABC) index is a degree-based topological index. It was introduced due to its applications in modeling the properties of certain molecular structures and has been since extensively studied. In this note, we examine the influence on the extremal values of the ABC index by various graph parameters. More specifically, we consider the maximum ABC index of connected graphs of given order, with fixed independence number, number of pendent vertices, chromatic number and edge-connectivity respectively. We provide characterizations of extremal structures as well as some conjectures. Numerical analysis of the extremal values is also presented.

Original language	English
Pages (from-to)	208-217
Number of pages	10
Journal	Discrete Applied Mathematics
Volume	215
DOIs	https://doi.org/10.1016/j.dam.2016.06.021
State	Published - Dec 31 2016

Keywords

Atom-bond connectivity index
Chromatic number
Edge-connectivity
Independence number
Pendent vertices

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10.1016/j.dam.2016.06.021

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title = "Maximum atom-bond connectivity index with given graph parameters",

abstract = "The atom-bond connectivity (ABC) index is a degree-based topological index. It was introduced due to its applications in modeling the properties of certain molecular structures and has been since extensively studied. In this note, we examine the influence on the extremal values of the ABC index by various graph parameters. More specifically, we consider the maximum ABC index of connected graphs of given order, with fixed independence number, number of pendent vertices, chromatic number and edge-connectivity respectively. We provide characterizations of extremal structures as well as some conjectures. Numerical analysis of the extremal values is also presented.",

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AU - Zhang, Xiu Mei

AU - Yang, Yu

AU - Wang, Hua

AU - Zhang, Xiao Dong

PY - 2016/12/31

Y1 - 2016/12/31

N2 - The atom-bond connectivity (ABC) index is a degree-based topological index. It was introduced due to its applications in modeling the properties of certain molecular structures and has been since extensively studied. In this note, we examine the influence on the extremal values of the ABC index by various graph parameters. More specifically, we consider the maximum ABC index of connected graphs of given order, with fixed independence number, number of pendent vertices, chromatic number and edge-connectivity respectively. We provide characterizations of extremal structures as well as some conjectures. Numerical analysis of the extremal values is also presented.

AB - The atom-bond connectivity (ABC) index is a degree-based topological index. It was introduced due to its applications in modeling the properties of certain molecular structures and has been since extensively studied. In this note, we examine the influence on the extremal values of the ABC index by various graph parameters. More specifically, we consider the maximum ABC index of connected graphs of given order, with fixed independence number, number of pendent vertices, chromatic number and edge-connectivity respectively. We provide characterizations of extremal structures as well as some conjectures. Numerical analysis of the extremal values is also presented.

KW - Atom-bond connectivity index

KW - Chromatic number

KW - Edge-connectivity

KW - Independence number

KW - Pendent vertices

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VL - 215

SP - 208

EP - 217

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Maximum atom-bond connectivity index with given graph parameters

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Keywords

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