Mathematical Properties and Computations of Banahatti indices for a Nano-Structure "Toroidal Polyhex Network"

Abstract: Let G be the connected graph with vertex set V(G) and edge set E(G).The first and second K Banhatti indices of G are defined as B1(G)=Σue[dG (u) +dG (e)] and B2(G)=Σue[dG (u) +dG (e)] where ue means that the vertex u and edge e are incident in G.The first and second K hyper Banhatti indices of G are defined as HB1(G) = Σue[dg(u) + dG (e)]2 and HB2(G) = Σue[dg(u) dG (e)]2 respectively . In this paper, we compute the first and second K Banhatti indices of toroidal polyhex network. In addition, the first and second K hyper Banhatti indices of toroidal polyhex networks are determined.