The Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains

As highly discriminant distance-based topological indices, the Balaban index and the sum-Balaban index of a graph G are defined as J(G)=fracmmu+1sumlimitsuvin E frac1sqrtDG(u)DG(v) and SJ(G)=fracmmu+1sumlimitsuvin E frac1sqrtDG(u)+DG(v), respectively, where DG(u)=sumlimitsvin Vd(u,v) is the distance sum of vertex u in G, m is the number of edges and $mu$ is the cyclomatic number of G. They are useful distance-based descriptor in chemometrics. In this paper, we focus on the extremal graphs of spiro and polyphenyl hexagonal chains with respect to the Balaban index and the sum-Balaban index.