University of KashanIranian Journal of Mathematical Chemistry2228-64899420181201The Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains2412547376310.22052/ijmc.2018.143823.1381ENY. ZuoCollege of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. ChinaY. TangCollege of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. ChinaH. Y. DengCollege of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. ChinaJournal Article20180809As highly discriminant distance-based topological indices, the Balaban index and the sum-Balaban index of a graph $G$ are defined as<br /> $J(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)D_{G}(v)}}$ and $SJ(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)+D_{G}(v)}}$, respectively, where $D_{G}(u)=sumlimits_{vin V}d(u,v)$ 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.http://ijmc.kashanu.ac.ir/article_73763_77c3dbe43fd89410f6e92ef2ba7b252a.pdf