Abstract

A benzenoid is a class of chemical compounds with at least one benzene ring(hexagon as a graph) and resonance bonds in the benzene ring give increased stability in benzenoids. A finite connected subgraph of the infinite hexagonal lattice without cut vertices or non-hexagonal interior faces is said to be a benzenoid system (or a hexagonal system) and these systems are geometric figures. Benzenoid systems are widely used because they are the representations of the skeletons (focussing on the structure induced by the carbon atoms) of molecules of benzenoid hydrocarbons.

The first and second Zagreb indices are among the most studied topological indices. We now consider analogous graph invariants, based on the second degrees of vertices, called Zagreb connection indices. The main objective of this paper is to compute these connection indices for six benzenoid systems(three catacondensed and three pericondensed systems). In the end, an application of the obtained results for these indices of some classes of benzenoid systems is also included. Mainly, a comparison among the Zagreb connection indices of some benzenoid systems is performed with the help of numerical tables and 3 D plots.

摘要

苯类化合物是一类具有至少一个苯环（图为六边形）的化合物，苯环中的共振键增加了苯类化合物的稳定性。没有切割顶点或非六边形内面的​​无限六边形晶格的有限连通子图被称为苯系系统（或六边形系统），这些系统是几何图形。苯系系统被广泛使用，因为它们代表了苯系烃分子的骨架（关注碳原子诱导的结构）。

第一和第二萨格勒布指数是研究最多的拓扑指数之一。我们现在考虑基于第二度顶点的类似图不变量，称为萨格勒布连接索引。本文的主要目的是计算六个苯系系统（三个catacondensed 和三个pericondensed 系统）的连接指数。最后，还包括了对某些类苯系统的这些指标的应用。主要是借助数值表和3D图对一些苯系系统的萨格勒布连接指数进行了比较。