Computing Fourth Atom-bond Connectivity Index of V-Phenylenic Nanotubes and Nanotori

Among topological descriptors connectivity topological indices are very important and they have a prominent role in chemistry. One of them is atom-bond connectivity (ABC) index defined as ABC(G) = Sigma root d(x)+d(y)-2/d(theta)d(theta), in which degree of vertex v denoted by d(v). Recently, a new version of atom-bond connectivity (ABC(4)) index was introduced by M. Ghorbani et. al in 2010 and is defined as ABC(4)(G) = Sigma root S-u+S-v-2/SuSv, where S-n = Sigma 15(NC(S)) and N-G(u) = {v is an element of V(G)vertical bar uv is an element of E(G)}. In this paper we compute this new topological index for V-Phenylenic Nanotube and Nanotori.