eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-12-01
9
4
241
254
10.22052/ijmc.2018.143823.1381
73763
The Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains
Y. Zuo
yzuo@163.com
1
Y. Tang
tang015@163.com
2
H. Y. Deng
hydeng@hunnu.edu.cn
3
College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China
College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China
College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China
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.
https://ijmc.kashanu.ac.ir/article_73763_77c3dbe43fd89410f6e92ef2ba7b252a.pdf
Balaban index
sum-Balaban index
spiro hexagonal chain, polyphenyl hexagonal chain
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-12-01
9
4
255
261
10.22052/ijmc.2017.51462.1186
45090
An application of geometrical isometries in non-planar molecules
A. Rezaei
a_rezaei@kashanu.ac.ir
1
A. Reisi-Vanani
areisi@kashanu.ac.ir
2
S. Masoum
masoum@kashanu.ac.ir
3
University of Kashan
University of Kashan
University of Kashan
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.
https://ijmc.kashanu.ac.ir/article_45090_b0e5726e71cd6e6f99f64bd79fa9d5a6.pdf
frame
isometry
orthogonal transformation
polygon
Non-planar polycyclic molecule
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-12-01
9
4
263
277
10.22052/ijmc.2017.72666.1265
81353
On ev-degree and ve-degree topological indices
B. Sahin
shnbnymn25@gmail.com
1
S. Ediz
suleymanediz@yyu.edu.tr
2
Faculty of Science, Selçuk University, Konya, Turkey
Faculty of Education, Yuzuncu Yil University, Van, Turkey
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.
https://ijmc.kashanu.ac.ir/article_81353_b1c7d097f932eb1537ce6797d7e1ed84.pdf
ev-degree
ve-degree
ev-degree topological indices
ve-degree topological indices
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-12-01
9
4
279
287
10.22052/ijmc.2017.81079.1277
81544
The second geometric-arithmetic index for trees and unicyclic graphs
N. Dehgardi
n.dehgardi@sirjantech.ac.ir
1
H. Aram
hamideh.aram@gmail.com
2
A. Khodkar
akhodkar@westga.edu
3
Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, Iran
Department of Mathematics, Gareziaeddin Center, Khoy Branch, Islamic Azad University, Khoy, Iran
Department of Mathematics, University of West Georgia, Carrollton GA 30082
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.
https://ijmc.kashanu.ac.ir/article_81544_d6ee54879d3b9af783c9e4a0e8b112b9.pdf
Second geometric-arithmetic index
Trees
Unicyclic graphs
eng
University of Kashan
Iranian Journal of Mathematical Chemistry
2228-6489
2008-9015
2018-12-01
9
4
289
299
10.22052/ijmc.2018.113339.1337
81558
On the saturation number of graphs
S. Alikhani
alikhani@yazd.ac.ir
1
N. Soltani
neda_soltani@ymail.com
2
Yazd University, iran
Yazd University, Iran
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.
https://ijmc.kashanu.ac.ir/article_81558_806cdc8af74e642c5afec1d82f3f77db.pdf
Maximal matching
Saturation number
corona