Wiener-type indices of Parikh word representable graphs

Abstract

A new class of graphs G(w), called Parikh word representable graphs (P W RG), corresponding to words w that are finite sequence of symbols, was considered in the recent past. Several properties of these graphs have been established. In this paper, we consider these graphs corresponding to binary core words of the form aub over a binary alphabet {a, b}. We derive formulas for computing the Wiener index of the P W RG of a binary core word. Sharp bounds are established on the value of this index in terms of different parameters related to binary words over {a, b} and the corresponding P W RGs. Certain other Wiener-type indices that are variants of Wiener index are also considered. Formulas for computing these indices in the case of P W RG of a binary core word are obtained.

On Exploring the Topological Aspects of the Chemical Structure of the Nanotube \(HAC_{5}C_{7}[w,t]\)

“…Furthermore, chemical graph theory has sparked interest in various topological indices associated with graphs, aiming to describe molecular structures in terms of these indices [23][24][25][26][27][28][29]. Numerous studies have provided formulas for computing these indices and established constraints on their values [30,31].…”

Certain Distance-Based Topological Indices of Parikh Word Representable Graphs

“…ere are a number of studies (for example, [21]) of various topological indices of graphs establishing formulae for computing the indices and also providing upper and lower bounds on the values of such indices. Recently, in [22], properties of one of the important topological indices, namely, Wiener index and some of its variants related to PWRGs of binary words, were studied. In this study, certain distance-based topological indices of PWRGs of binary core words are investigated.…”