Zagreb Connection Indices for Some Benzenoid Systems

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.