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.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64899420181014An application of geometrical isometries in non-planar molecules2552614509010.22052/ijmc.2017.51462.1186ENA. A.RezaeiUniversity of KashanA. Reisi-VananiUniversity of KashanS. MasoumUniversity of KashanJournal Article20160406In this paper we introduce a novel methodology to transmit the<br /> origin to the center of a polygon in a molecule structure such that the<br /> special axis be perpendicular to the plane containing the polygon. The<br /> mathematical calculation are described completely and the algorithm<br /> will be showed as a computer program.http://ijmc.kashanu.ac.ir/article_45090_0c62e88dc5cc7c0a6eec5722a06c2947.pdf