1. Wiener-type indices of Parikh word representable graphs
- Author
-
K. G. Subramanian, Nobin Thomas, Lisa Mathew, and Sastha Sriram
- Subjects
Algebra and Number Theory ,Binary number ,Value (computer science) ,Of the form ,0102 computer and information sciences ,02 engineering and technology ,Wiener index ,Type (model theory) ,01 natural sciences ,Theoretical Computer Science ,Combinatorics ,Index (publishing) ,010201 computation theory & mathematics ,Core (graph theory) ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,020201 artificial intelligence & image processing ,Geometry and Topology ,Computer Science::Formal Languages and Automata Theory ,Word (group theory) ,Mathematics - Abstract
A new class of graphs G(w), called Parikh word representable graphs (PWRG), 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 PWRG 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 PWRGs. Certain other Wiener-type indices that are variants of Wiener index are also considered. Formulas for computing these indices in the case of PWRG of a binary core word are obtained.
- Published
- 2021