PI and weighted PI indices for powers of paths, cycles, and their complements

Article type: Research Article

Authors: Manju, S.C. | Geetha, J. | Somasundaram, K.

Affiliations: [a] Department of Mathematics, Amrita Vishwa Vidyapeetham, Kochi, India | [b] Department of Mathematics, Amrita School of Physical Sciences, Amrita Vishwa Vidyapeetham, Coimbatore, India

Correspondence: [*] Corresponding author. K. Somasundaram. E-mail: s_sundaram@cb.amrita.edu.

Abstract:  Topological indices play a significant role in molecular chemistry, spectral graph theory, network theory, etc. We aim to contribute some new results on PI and weighted PI indices. The vertex PI index of a graph G is given by, PI(G) = ∑e∈E(G)(|V(G) | - NG(e)). The weighted PI index of a graph G is given by, PIw(G) = ∑e=(u,v)∈E(G)(dG(u) + dG(v))(|V(G) | - NG(e)). We obtained the PI and weighted PI indices for powers of paths, cycles, and their complements in this study. Also, for a regular graph, a relationship between PI and weighted PI indices is established, and using this relation the weighted PI index is calculated for kth power of a cycle.

Keywords: PI index, Weighted PI index, Power of a graph, Complement of a graph., AMS subject classification: 05C07, 05C09, 05C12.

DOI: 10.3233/JIFS-221436

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 1, pp. 1439-1452, 2023