The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices
Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Chengdu University, Chengdu 610106, China
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
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
The Cartesian product and join are two classical operations in graphs. Let
be the degree of a vertex
in line graph
of a graph
. The edge versions of atom-bond connectivity (
) and geometric arithmetic (
) indices of G
are defined as
, respectively. In this paper,
indices for certain Cartesian product graphs (such as
) are obtained. In addition,
indices of certain join graphs (such as
) are deduced. Our results enrich and revise some known results.
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which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
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.
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(7):1731.
Zhang, Xiujun; Jiang, Huiqin; Liu, Jia-Bao; Shao, Zehui. 2018. "The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices." Molecules 23, no. 7: 1731.
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