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

• Published in: Journal of intelligent & fuzzy systems Vol. 44; no. 1; pp. 1439 - 1452
• Main Authors: Manju, S.C., Geetha, J., Somasundaram, K.
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.01.2023; Sage Publications Ltd
• Subjects: Graph theory; PI index; Complement of a graph; Weighted PI index; AMS subject classification: 05C07, 05C09, 05C12; Power of a graph
• ISSN: 1064-1246; 1875-8967
• DOI: 10.3233/JIFS-221436

 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) | - N G (e)). The weighted PI index of a graph G is given by, PI w (G) = ∑e=(u,v)∈E(G)(d G (u) + d G (v))(|V(G) | - N G (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 k th power of a cycle.