University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
9
4
2018
12
01
The Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains
241
254
EN
Y.
Zuo
College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China
yzuo@163.com
Y.
Tang
College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China
tang015@163.com
H. Y.
Deng
College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China
hydeng@hunnu.edu.cn
10.22052/ijmc.2018.143823.1381
As 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.
Balaban index,sum-Balaban index,spiro hexagonal chain, polyphenyl hexagonal chain
https://ijmc.kashanu.ac.ir/article_73763.html
https://ijmc.kashanu.ac.ir/article_73763_77c3dbe43fd89410f6e92ef2ba7b252a.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
9
4
2018
12
01
An application of geometrical isometries in non-planar molecules
255
261
EN
A.
A.
Rezaei
University of Kashan
a_rezaei@kashanu.ac.ir
A.
Reisi-Vanani
University of Kashan
areisi@kashanu.ac.ir
S.
Masoum
University of Kashan
masoum@kashanu.ac.ir
10.22052/ijmc.2017.51462.1186
In 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.
frame,isometry,orthogonal transformation,polygon,Non-planar polycyclic molecule
https://ijmc.kashanu.ac.ir/article_45090.html
https://ijmc.kashanu.ac.ir/article_45090_b0e5726e71cd6e6f99f64bd79fa9d5a6.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
9
4
2018
12
01
On ev-degree and ve-degree topological indices
263
277
EN
B.
Sahin
Faculty of Science, Selçuk University, Konya, Turkey
shnbnymn25@gmail.com
S.
Ediz
Faculty of Education, Yuzuncu Yil University, Van, Turkey
suleymanediz@yyu.edu.tr
10.22052/ijmc.2017.72666.1265
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<br /> definitions of Zagreb and Randić indices. It was shown that ev-degree and ve-degree topological indices can be<br /> used as possible tools in QSPR researches . In this paper we define the ve-degree and ev-degree Narumi–Katayama<br /> indices, investigate the predicting power of these novel indices and extremal graphs with respect to these novel<br /> topological indices. Also we give some basic mathematical properties of ev-degree and ve-degree NarumiKatayama and Zagreb indices.
ev-degree,ve-degree,ev-degree topological indices,ve-degree topological indices
https://ijmc.kashanu.ac.ir/article_81353.html
https://ijmc.kashanu.ac.ir/article_81353_b1c7d097f932eb1537ce6797d7e1ed84.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
9
4
2018
12
01
The second geometric-arithmetic index for trees and unicyclic graphs
279
287
EN
N.
Dehgardi
Department of Mathematics and Computer Science, Sirjan University of Technology,
Sirjan, Iran
n.dehgardi@sirjantech.ac.ir
H.
Aram
Department of Mathematics,
Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran
hamideh.aram@gmail.com
A.
Khodkar
Department of Mathematics, University of West Georgia, Carrollton GA 30082
akhodkar@westga.edu
10.22052/ijmc.2017.81079.1277
Let $G$ be a finite and simple graph with edge set $E(G)$. The<br /> second geometric-arithmetic index is defined as<br /> $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$,<br /> where $n_u$ denotes the number of vertices in $G$ lying closer to<br /> $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms<br /> of the order and maximum degree of the tree. We also find a sharp upper bound for $GA_2(G)$, where $G$<br /> is a unicyclic graph, in terms of the order, maximum degree and girth of $G$.<br /> In addition, we characterize the trees and unicyclic graphs which achieve the upper bounds.
Second geometric-arithmetic index,Trees,Unicyclic graphs
https://ijmc.kashanu.ac.ir/article_81544.html
https://ijmc.kashanu.ac.ir/article_81544_d6ee54879d3b9af783c9e4a0e8b112b9.pdf
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
9
4
2018
12
01
On the saturation number of graphs
289
299
EN
S.
Alikhani
Yazd University, iran
alikhani@yazd.ac.ir
N.
Soltani
Yazd University, Iran
neda_soltani@ymail.com
10.22052/ijmc.2018.113339.1337
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 $s(G)$. <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.
Maximal matching,Saturation number,corona
https://ijmc.kashanu.ac.ir/article_81558.html
https://ijmc.kashanu.ac.ir/article_81558_806cdc8af74e642c5afec1d82f3f77db.pdf