research-article

Maximum atom-bond connectivity index with given graph parameters

Authors:

Xiao-Dong ZhangAuthors Info & Claims

Discrete Applied Mathematics, Volume 215, Issue C

Pages 208 - 217

https://doi.org/10.1016/j.dam.2016.06.021

Published: 31 December 2016 Publication History

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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Cited By

(2019)The maximum atom-bond connectivity index for graphs with edge-connectivity oneDiscrete Applied Mathematics10.1016/j.dam.2016.12.011220:C(170-173)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.dam.2016.12.011
Dimitrov DIkica Bkrekovski R(2017)Remarks on maximum atom-bond connectivity index with given graph parametersDiscrete Applied Mathematics10.1016/j.dam.2017.01.019222:C(222-226)Online publication date: 11-May-2017
https://dl.acm.org/doi/10.1016/j.dam.2017.01.019
Shao ZWu PGao YGutman IZhang X(2017)On the maximum ABC index of graphs without pendent verticesApplied Mathematics and Computation10.1016/j.amc.2017.07.075315:C(298-312)Online publication date: 15-Dec-2017
https://dl.acm.org/doi/10.1016/j.amc.2017.07.075

Maximum atom-bond connectivity index with given graph parameters
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory
2. Theory of computation

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On atom-bond connectivity index of connected graphs

The atom-bond connectivity (ABC) index of a graph G is defined as ABC(G)=@?uv@?E(G)d"u+d"v-2d"ud"v, where E(G) is the edge set and d"u is the degree of vertex u of G. We give an upper bound for the ABC index of connected graphs with fixed number of ...
Remarks on maximum atom-bond connectivity index with given graph parameters

The atom-bond connectivity (ABC) index is a degree-based molecular structure descriptor that can be used for modelling thermodynamic properties of organic chemical compounds. Motivated by its applicable potential, a series of investigations have been ...
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The atom-bond connectivity (ABC) index of a graph G is defined as ABC(G)=@?uv@?E(G)d"u+d"v-2d"ud"v, where E(G) is the edge set and d"u is the degree of vertex u of G. We give the best upper bound for the ABC index of trees with a perfect matching, and ...

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Published In

cover image Discrete Applied Mathematics

Discrete Applied Mathematics Volume 215, Issue C

December 2016

239 pages

ISSN:0166-218X

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Copyright © Elsevier B.V.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 31 December 2016

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Cited By

(2019)The maximum atom-bond connectivity index for graphs with edge-connectivity oneDiscrete Applied Mathematics10.1016/j.dam.2016.12.011220:C(170-173)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.dam.2016.12.011
Dimitrov DIkica Bkrekovski R(2017)Remarks on maximum atom-bond connectivity index with given graph parametersDiscrete Applied Mathematics10.1016/j.dam.2017.01.019222:C(222-226)Online publication date: 11-May-2017
https://dl.acm.org/doi/10.1016/j.dam.2017.01.019
Shao ZWu PGao YGutman IZhang X(2017)On the maximum ABC index of graphs without pendent verticesApplied Mathematics and Computation10.1016/j.amc.2017.07.075315:C(298-312)Online publication date: 15-Dec-2017
https://dl.acm.org/doi/10.1016/j.amc.2017.07.075

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