Reformulated Zagreb Indices of Some Cycle-Related Graphs and Linear [n]-Phenylenes

Abstract

Graph invariants (topological indices) are numerical values of graphs obtained from 2-dimensional (2-D) images of chemical structures. These invariants are used in the structure-property/activity studies to predict certain properties such as the enthalpy of vaporization, and stability of molecular structures. In this paper, reformulated Zagreb indices, which are edge-degree-based indices, are considered. First, the reformulated Zagreb indices for cycle-related graphs which are wheel, helm, gear, friendship, closed helm, flower, sun, and sunflower are computed. The values of the first and second reformulated Zagreb indices of cycle-related these graphs and also the values of reformulated Zagreb indices of graphs with the same edge cardinality among studied graphs are compared numerically with the MATLAB software program. Finally, reformulated first Zagreb index and reformulated second Zagreb index of linear [n]-phenylenes are calculated and these values are computed numerically.