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

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 are defined as ∑ef∈E(L(G))dL(G)(e)+dL(G)(f)-2dL(G)(e)×dL(G)(f)...

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Bibliographic Details
Published in:Molecules (Basel, Switzerland) Switzerland), 2018-07, Vol.23 (7), p.1731
Main Authors: Zhang, Xiujun, Jiang, Huiqin, Liu, Jia-Bao, Shao, Zehui
Format: Article
Language:English
Subjects:
Arithmetic
atom-bond connectivity index
Cartesian coordinates
Cartesian product graph
Connectivity
geometric arithmetic index
Graphs
join graph
line graph
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Summary: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 are defined as ∑ef∈E(L(G))dL(G)(e)+dL(G)(f)-2dL(G)(e)×dL(G)(f) and ∑ef∈E(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 Pn□Pm, Pn□Cm and Pn□Sm) 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.
ISSN:1420-3049
1420-3049
DOI:10.3390/molecules23071731