2019-10-22T05:00:25Z
http://ijmc.kashanu.ac.ir/?_action=export&rf=summon&issue=9369
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2018
9
4
The Extremal Graphs for (Sum-) Balaban Index of Spiro and Polyphenyl Hexagonal Chains
Y.
Zuo
Y.
Tang
H. Y.
Deng
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
2018
12
01
241
254
http://ijmc.kashanu.ac.ir/article_73763_77c3dbe43fd89410f6e92ef2ba7b252a.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2018
9
4
An application of geometrical isometries in non-planar molecules
A.
Rezaei
A.
Reisi-Vanani
S.
Masoum
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
2018
12
01
255
261
http://ijmc.kashanu.ac.ir/article_45090_b0e5726e71cd6e6f99f64bd79fa9d5a6.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2018
9
4
On ev-degree and ve-degree topological indices
B.
Sahin
S.
Ediz
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
2018
12
01
263
277
http://ijmc.kashanu.ac.ir/article_81353_b1c7d097f932eb1537ce6797d7e1ed84.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2018
9
4
The second geometric-arithmetic index for trees and unicyclic graphs
N.
Dehgardi
H.
Aram
A.
Khodkar
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
2018
12
01
279
287
http://ijmc.kashanu.ac.ir/article_81544_d6ee54879d3b9af783c9e4a0e8b112b9.pdf
Iranian Journal of Mathematical Chemistry
Iranian J. Math. Chem.
2228-6489
2228-6489
2018
9
4
On the saturation number of graphs
S.
Alikhani
N.
Soltani
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
2018
12
01
289
299
http://ijmc.kashanu.ac.ir/article_81558_806cdc8af74e642c5afec1d82f3f77db.pdf