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

Topological 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)=respectively, where d_u is the degree of the vertex u. The aim of this paper is to introduced the new versions of ABC index and GA index 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 Opq, the hexagonal grid H(p, q) and the square grid G_{p, q}. Also, we compared these results obtained with the ones by other indices like the ABC₄ index and the GA₅ index.