%0 Journal Article
%T The Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains
%J Iranian Journal of Mathematical Chemistry
%I University of Kashan
%Z 2228-6489
%A Zuo, Y.
%A Tang, Y.
%A Deng, H. Y.
%D 2018
%\ 12/01/2018
%V 9
%N 4
%P 241-254
%! The Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains
%K Balaban index
%K sum-Balaban index
%K spiro hexagonal chain, polyphenyl hexagonal chain
%R 10.22052/ijmc.2018.143823.1381
%X As highly discriminant distance-based topological indices, the Balaban index and the sum-Balaban index of a graph $G$ are defined as $J(G)=\frac{m}{\mu+1}\sum\limits_{uv\in E} \frac{1}{\sqrt{D_{G}(u)D_{G}(v)}}$ and $SJ(G)=\frac{m}{\mu+1}\sum\limits_{uv\in E} \frac{1}{\sqrt{D_{G}(u)+D_{G}(v)}}$, respectively, where $D_{G}(u)=\sum\limits_{v\in V}d(u,v)$ 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.
%U https://ijmc.kashanu.ac.ir/article_73763_77c3dbe43fd89410f6e92ef2ba7b252a.pdf