Computing multiple ABC index and multiple GA index of some grid graphs

Abstract

AbstractTopological indices are the atomic descriptors that portray the structures of chemical compounds and they help us to anticipate certain physico-compound properties like boiling point, enthalpy of vaporization and steadiness. The atom bond connectivity (ABC) index and geometric arithmetic (GA) index are topological indices which are defined as$ABC(G)=\sum_{uv\in E(G)}\sqrt{\frac{d_u+d_v-2}{d_ud_v}}$and$GA(G)=\sum_{uv\in E(G)}\frac{2\sqrt{d_ud_v}}{d_u+d_v}$, respectively, whereduis the degree of the vertexu. The aim of this paper is to introduced the new versions ofABCindex andGAindex namely multiple atom bond connectivity (ABC) index and multiple geometric arithmetic (GA) index. As an application, we have computed these newly defined indices for the octagonal grid$O_p^q$, the hexagonal gridH(p,q) and the square gridGp, q. Also, we compared these results obtained with the ones by other indices like theABC4index and theGA5index.