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 d L (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 ( A B C e ) and geometric arithmetic ( G A e ) indices of G are defined as ∑ e f ∈ E (L (G)) d L (G) (e) + d L (G) (f) − 2 d L (G) (e) × d L (G) (f) and ∑ e f ∈ E (L (G)) 2 d L (G) (e) × d L (G) (f) d L (G) (e) + d L (G) (f) , respectively. In this paper, A B C e and G A e indices for certain Cartesian product graphs (such as P n □ P m , P n □ C m and P n □ S m ) are obtained. In addition, A B C e and G A e indices of certain join graphs (such as C m + P n + S r , P m + P n + P r , C m + C n + C r and S m + S n + S r ) are deduced. Our results enrich and revise some known results. [ABSTRACT FROM AUTHOR]