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 /> $J(G)=\frac{m}{\mu+1}\sum\limits_{uv\in E} \frac{1}{\sqrt{D_{G}(u)D_{G}(v)}}$ 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.https://ijmc.kashanu.ac.ir/article_73763_77c3dbe43fd89410f6e92ef2ba7b252a.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64899420181201An 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 origin to the center of a polygon in a molecule structure such that the special axis be perpendicular to the plane containing the polygon. The<br /> mathematical calculation are described completely and the algorithm will be showed as a computer program.https://ijmc.kashanu.ac.ir/article_45090_b0e5726e71cd6e6f99f64bd79fa9d5a6.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64899420181201On Ev-degree and Ve-degree Topological Indices2632778135310.22052/ijmc.2017.72666.1265ENB.SahinFaculty of Science, Selçuk University, Konya, TurkeyS.EdizFaculty of Education, Yuzuncu Yil University, Van, TurkeyJournal Article20170110Recently two new degree concepts have been defined in graph theory: ev-degree and ve-degree. Also the evdegree and ve-degree Zagreb and Randić indices have been defined very recently as parallel of the classical definitions of Zagreb and Randić indices. It was shown that ev-degree and ve-degree topological indices can be used as possible tools in QSPR researches . In this paper we define the ve-degree and ev-degree Narumi–Katayama indices, investigate the predicting power of these novel indices and extremal graphs with respect to these novel topological indices. Also we give some basic mathematical properties of ev-degree and ve-degree NarumiKatayama and Zagreb indices.https://ijmc.kashanu.ac.ir/article_81353_b1c7d097f932eb1537ce6797d7e1ed84.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64899420181201The Second Geometric-arithmetic Index for Trees and Unicyclic Graphs2792878154410.22052/ijmc.2017.81079.1277ENN.DehgardiDepartment of Mathematics and Computer Science, Sirjan University of Technology,
Sirjan, IranH.AramDepartment of Mathematics,
Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, IranA.KhodkarDepartment of Mathematics, University of West Georgia, Carrollton GA 30082Journal Article20170401Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=\sum_{uv\in E(G)}\frac{2\sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree of the tree. We also find a sharp upper bound for $GA_2(G)$, where $G$ is a unicyclic graph, in terms of the order, maximum degree and girth of $G$. In addition, we characterize the trees and unicyclic graphs which achieve the upper bounds.https://ijmc.kashanu.ac.ir/article_81544_d6ee54879d3b9af783c9e4a0e8b112b9.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64899420181201On the Saturation Number of Graphs2892998155810.22052/ijmc.2018.113339.1337ENS.AlikhaniYazd University, iranN.SoltaniYazd University, IranJournal Article20180105Let $G=(V,E)$ be a simple connected graph. A matching $M$ in a graph $G$ is a collection of edges of $G$ such that no two edges from $M$ share a vertex. A matching $M$ is maximal if it cannot be extended to a larger matching in $G$. The cardinality of any smallest maximal matching in $G$ is the saturation number of $G$ and is denoted by $s(G)$. <br /> In this paper we study the saturation number of the corona product of two specific graphs. We also consider some graphs with certain constructions that are of importance in chemistry and study their saturation number.https://ijmc.kashanu.ac.ir/article_81558_806cdc8af74e642c5afec1d82f3f77db.pdf