The Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains
Y.
Zuo
College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China
author
Y.
Tang
College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China
author
H. Y.
Deng
College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China
author
text
article
2018
eng
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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
9
v.
4
no.
2018
241
254
http://ijmc.kashanu.ac.ir/article_73763_77c3dbe43fd89410f6e92ef2ba7b252a.pdf
dx.doi.org/10.22052/ijmc.2018.143823.1381
An application of geometrical isometries in non-planar molecules
A.
Rezaei
University of Kashan
author
A.
Reisi-Vanani
University of Kashan
author
S.
Masoum
University of Kashan
author
text
article
2018
eng
In 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 mathematical calculation are described completely and the algorithm will be showed as a computer program.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
9
v.
4
no.
2018
255
261
http://ijmc.kashanu.ac.ir/article_45090_b0e5726e71cd6e6f99f64bd79fa9d5a6.pdf
dx.doi.org/10.22052/ijmc.2017.51462.1186
On ev-degree and ve-degree topological indices
B.
Sahin
Faculty of Science, Selçuk University, Konya, Turkey
author
S.
Ediz
Faculty of Education, Yuzuncu Yil University, Van, Turkey
author
text
article
2018
eng
Recently 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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
9
v.
4
no.
2018
263
277
http://ijmc.kashanu.ac.ir/article_81353_b1c7d097f932eb1537ce6797d7e1ed84.pdf
dx.doi.org/10.22052/ijmc.2017.72666.1265
The second geometric-arithmetic index for trees and unicyclic graphs
N.
Dehgardi
Department of Mathematics and Computer Science, Sirjan University of Technology,
Sirjan, Iran
author
H.
Aram
Department of Mathematics,
Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran
author
A.
Khodkar
Department of Mathematics, University of West Georgia, Carrollton GA 30082
author
text
article
2018
eng
Let $G$ 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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
9
v.
4
no.
2018
279
287
http://ijmc.kashanu.ac.ir/article_81544_d6ee54879d3b9af783c9e4a0e8b112b9.pdf
dx.doi.org/10.22052/ijmc.2017.81079.1277
On the saturation number of graphs
S.
Alikhani
Yazd University, iran
author
N.
Soltani
Yazd University, Iran
author
text
article
2018
eng
Let $G=(V,E)$ 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 $s(G)$. 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.
Iranian Journal of Mathematical Chemistry
University of Kashan
2228-6489
9
v.
4
no.
2018
289
299
http://ijmc.kashanu.ac.ir/article_81558_806cdc8af74e642c5afec1d82f3f77db.pdf
dx.doi.org/10.22052/ijmc.2018.113339.1337