M-Polynomials and Topological Indices for Line Graphs of Chain Silicate Network and H-Naphtalenic Nanotubes

Abstract

Graph theory has provided a very useful tool, called topological index, which is a number from the graph M with the property that every graph N isomorphic to M value of a topological index must be same for both M and N. Topological index is a descriptor in graph theory which is used to quantify the physio-chemical properties of the chemical graph. In this paper, we computed closed forms of M-polynomials for line graphs of H-naphtalenic nanotubes and chain silicate network. From M-polynomial, we obtained some topological indices based on degrees.

Topological Indices of Pent-Heptagonal Nanosheets via M-Polynomials

“…In 2020, Khalaf et al [38] computed the M-polynomial and topological indices of book graph and Raza and Sakaiti [2] solved the M-polynomial and degree-based topological indices of some nanostructures. In 2021, Mondal et al [39] find out the neighborhood M-polynomial of titanium compounds and Irfan et al [1] computed the M-polynomials and topological indices for line graphs of chain silicate network and H-naphtalenic nanotubes.…”

“…Nanostructures [1,2] have been studied as new materials with the size of elementals structures that has been engineered at the nanometers' scale. Most of the materials in this size range usually show novel behavior.…”

A new perspective on the modeling and topological characterization of H-Naphtalenic nanosheets with applications

“…In [ 38 – 42 ], the topological properties of H-Naphtalenic nanosheets are studied. Jane Olive Sharon et al investigated the transmission of every vertex in H-Naphtalenic nanosheet [ 43 ]. In [ 13 , 44 ], scientists investigated the topological modeling and characterization of antiviral medications used for the COVID-19 treatment, such as bevacizumab, hydroxy chloroquine, umifenovir, ritonavir, remdesivir, nafamostat, theaflavin, lopinavir and camostat.…”

M-Polynomials and Associated Topological Indices of Sodalite Materials

“…As we know that the study of M-polynomial is a very useful combination of numerical descriptors and algebraic theory, for the study of chemical networks, one can find an intense study on this topic; very particular and selected articles are cited here. Nanotube-related networks or structures were studied in [17][18][19], M-polynomials for different generalized families of graphs were discussed in [20][21][22], convex polytopes were studied in [23], chemical benzenoid structures were discussed in [24], a fine relation of M-polynomial with the probabilistic theory was discussed in [25], the study of this topic on metal organic structure was detailed in [26,27], and some computer-related networks in terms of M-polynomials can be found in [28,29]; there are many types of polynomials, and one of the varieties can be found in [30].…”