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Molecules 2018, 23(7), 1731; https://doi.org/10.3390/molecules23071731

The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices

1
Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Chengdu University, Chengdu 610106, China
2
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
3
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
*
Author to whom correspondence should be addressed.
Received: 25 May 2018 / Revised: 27 June 2018 / Accepted: 6 July 2018 / Published: 16 July 2018
(This article belongs to the Special Issue Molecular Computing and Bioinformatics)
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Abstract

The Cartesian product and join are two classical operations in graphs. Let dL(G)(e) be the degree of a vertex e in line graph L(G) of a graph G. The edge versions of atom-bond connectivity (ABCe) and geometric arithmetic (GAe) indices of G are defined as efE(L(G))dL(G)(e)+dL(G)(f)2dL(G)(e)×dL(G)(f) and efE(L(G))2dL(G)(e)×dL(G)(f)dL(G)(e)+dL(G)(f), respectively. In this paper, ABCe and GAe indices for certain Cartesian product graphs (such as PnPm, PnCm and PnSm) are obtained. In addition, ABCe and GAe indices of certain join graphs (such as Cm+Pn+Sr, Pm+Pn+Pr, Cm+Cn+Cr and Sm+Sn+Sr) are deduced. Our results enrich and revise some known results. View Full-Text
Keywords: line graph; Cartesian product graph; join graph; atom-bond connectivity index; geometric arithmetic index line graph; Cartesian product graph; join graph; atom-bond connectivity index; geometric arithmetic index
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Zhang, X.; Jiang, H.; Liu, J.-B.; Shao, Z. The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices. Molecules 2018, 23, 1731.

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