M-polynomial and topological indices of some transformed networks

Abstract

<abstract><p>In the chemical industry, topological indices play an important role in defining the properties of chemical compounds. They are numerical parameters and structure invariant. It is a proven fact by scientists that topological properties are influential tools for interconnection networks. In this paper, we will use stellation, medial and bounded dual operations to build transformed networks from zigzag and triangular benzenoid structures. Using M-polynomial, we compute the first and second Zagreb indices, second modified Zagreb indices, symmetric division index, general Randic index, reciprocal general Randic index. We also calculate atomic bond connectivity index, geometric arithmetic index, harmonic index, first and second Gourava indices, first and second hyper Gourava indices.</p></abstract>

Graphical Invariants for some Transformed Networks

“…Siddiqui et al worked on Zagreb indices and Zagreb polynomials of some nanostar dendrimers [34]. Yu et al defined indices through M-polynomial [37]. There are thousands of topological indices developed over the decades in the field of chemical graph theory.…”

Further study of eccentricity based indices for benzenoid hourglass network

“…Liu et al defined many indices in [ 7 ]. In 2019, Tanveer et al worked on M. polynomials [ 8 ], and in 2021 Yu et al also discussed topological properties in [ 9 ], some other indices are computed in [ 10 ].…”

Topological Characterization of Hexagonal Network and Non-Kekulean Benzenoid Hydrocarbon

“…Based on vertex degrees, the idea of Randic (R), atom-bond connectivity (ABC), and geometric-arithmetic (GA) topological indices was formed in chemical graph theory. This theory is related to quantitative analysis, statistics, topology, and complex mathematics [27,29]. In addition to graph models, such dynamic systems can be modeled using multi-agent systems, Markov chain and/or petri-nets, [4,5,11,18].…”