About Atom Bond Connectivity and Geometric-Arithmetic Indices of Special Chemical Molecular and Nanotubes - Farahani, Mohammad Reza; Husin, Mohamad Nazri; Nazeer, Waqas (Journal of Informatics and Mathematical Sciences, 2018)
Among topological descriptors connectivity indices are very important and they have a prominent role in chemistry. Two useful of them are the geometric-arithmetic (GA) and atom-bond connectivity (ABC) indices and are defined as \(GA(G)=_uvE(G)2d_u d_v d_u +d_v \) and \(ABC(G)=_e=uvE(G)d_u +d_v -2d_u d_v \), in which \(d_u\) and \(d_v\) are the degrees of the vertices \(u\) and \(v\), respectively. n this paper we compute these connectivity topological indices for a special chemical molecular graph ``Cas(C)-CaR(C)[m,n,p] Nanotubes Junction’’ are given. The Cas(C)-CaR(C)[m,n,p] Nanotubes Junction is a new nano-structure that was defined by M.V. Diudea, on based the new graph operations (Leapfrog Le and Capra Ca) on the cycle graph \(C_n\).