The Cartesian Product and Join Graphs on Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices
2018
Xiujun Zhang | Huiqin Jiang | Jia-Bao Liu | Zehui Shao
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 &sum:ef&isin:E(L(G))dL(G)(e)+dL(G)(f)&minus:2dL(G)(e)×:dL(G)(f) and &sum:ef&isin: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.
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