Two Classes of Topological Indices of Phenylene Molecule Graphs

Abstract

A phenylene is a conjugated hydrocarbons molecule composed of six- and four-membered rings. The matching energy of a graphGis equal to the sum of the absolute values of the zeros of the matching polynomial ofG, while the Hosoya index is defined as the total number of the independent edge sets ofG. In this paper, we determine the extremal graph with respect to the matching energy and Hosoya index for all phenylene chains.

New Formulas and New Bounds for the First and Second Zagreb Indices of Phenylenes

“…A lineer phenylene chain b. A zigzag phenylene chain (Wu, 2016) In the graph structure of a chemical structure, the vertices represent atoms and the edges represent chemical bonds and a numerical value calculated mathematically using a molecular graph is called a topological index (Rashid et al, 2022). Topological indices based on degree and distance are highly used in the mathematical process of combining chemical structure with physical attributes, chemical reactivity or biological activity (Jacob et al, 2023).…”

The expected values of arithmetic bond connectivity and geometric indices in random phenylene chains

“…In [34] the extremal phenylene chains with respect to Kirchhoff index and degree based topological indices have been characterized. For more details one may see [35] , [36] , [37] , [38] , [39] , [40] , [41] , [42] . In this paper, we extend the study of this class of hydrocarbon for four different types of indices namely, ABC, GA and the Zagreb indices and give their expected values for the same probability and outlines a details comparison between these indices with respect to the random phenylene chains.…”

Extremal Matching Energy of Random Polyomino Chains

“…The matching energy has received a lot of attention from researchers in recent years (see [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]). …”