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Article type: Research Article
Authors: Manju, S.C.a; * | Swarnajyothi, K.b | Geetha, J.b | Somasundaram, K.b
Affiliations: [a] Department of Mathematics, Amrita School of Arts and Sciences, Kochi, Amrita Vishwa Vidyapeetham, India Department of Science and Humanities, Sree Narayana Gurukulam college of Engineering, Kolenchery, India | [b] Department of Mathematics, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, India
Correspondence: [*] Corresponding author S.C. Manju, Department of Science and Humanities, Sree Narayana Gurukulam college of Engineering, Kolenchery, India. E-mail: manjuchithrabhanu@gmail.com.
Abstract: The Padmakar-Ivan (PI) index of a connected graph G is given by PI (G) = ∑e=(u,v)∈E(G) (|V (G) | - NG (e)) and weighted Padmakar-Ivan index is PIw (G) = ∑e=(u,v)∈E(G) (dG (u) + dG (v)) (|V (G) | - NG (e)) . In this paper, we present the PI index for various classes of perfect graphs, including block graphs, the line graph of unicyclic graphs, and split graphs. The theorems established in this study are applied to ascertain the PI index of chain and cyclic silicates. Furthermore, we derive both the PI and weighted PI indices for the lexicographic product of two regular graphs and determine the exact values for the lexicographic product involving a regular graph and a complete multipartite graph.
Keywords: PI index, weighted pi index, perfect graphs, block graphs, lexicographic product, regular graphs, chain and cyclic tetrahedral frameworks
DOI: 10.3233/JIFS-238204
Journal: Journal of Intelligent & Fuzzy Systems, vol. Pre-press, no. Pre-press, pp. 1-13, 2024
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