فهرست مطالب

Mathematical Chemistry - Volume:9 Issue:4, 2018
  • Volume:9 Issue:4, 2018
  • تاریخ انتشار: 1397/09/24
  • تعداد عناوین: 5
|
  • Y. Zuo, Y. Tang, H. Y. Deng * Pages 241-254
    $J(G)=\frac{m}{\mu+1}\sum\limits_{uv\in E} \frac{1}{\sqrt{D_{G}(u)D_{G}(v)}}$ 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.
    Keywords: Balaban index, sum-Balaban index, spiro hexagonal chain, polyphenyl hexagonal chain
  • A. A. Rezaei *, A. Reisi, Vanani, S. Masoum Pages 255-261
    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.
    Keywords: frame, isometry, orthogonal transformation, polygon, Non-planar polycyclic molecule
  • B. Sahin *, S. Ediz Pages 263-277
    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.
    Keywords: ev-degree, ve-degree, ev-degree topological indices, ve-degree topological indices
  • N. Dehgardi, H. Aram, A. Khodkar* Pages 279-287
    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.
    Keywords: Second geometric-arithmetic index, trees, unicyclic graphs
  • S. Alikhani *, N. Soltani Pages 289-299
    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.
    Keywords: Maximal matching, Saturation number, Corona