Relating graph structures with words which are finite sequences of symbols, Parikh word representable graphs (PWRGs) were introduced. On the other hand, in chemical graph theory, graphs have been associated with molecular structures. Also, several topological indices have been defined in terms of graph parameters and studied for different classes of graphs. In this study, we derive expressions for computing certain topological indices of PWRGs of binary core words, thereby enriching the study of PWRGs.
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.
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