{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:59:44Z","timestamp":1777705184071,"version":"3.51.4"},"reference-count":11,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2023,1,5]]},"abstract":"<jats:p>\u00a0Topological 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)\u00a0=\u00a0\u2211e\u2208E(G)(|V(G)\u00a0|\u00a0-\u00a0NG(e)). The weighted PI index of a graph G is given by, PIw(G)\u00a0=\u00a0\u2211e=(u,v)\u2208E(G)(dG(u)\u00a0+\u00a0dG(v))(|V(G)\u00a0|\u00a0-\u00a0NG(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.<\/jats:p>","DOI":"10.3233\/jifs-221436","type":"journal-article","created":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T11:23:26Z","timestamp":1666092206000},"page":"1439-1452","source":"Crossref","is-referenced-by-count":2,"title":["PI and weighted PI indices for powers of paths, cycles, and their complements"],"prefix":"10.1177","volume":"44","author":[{"given":"S.C.","family":"Manju","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Geetha","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K.","family":"Somasundaram","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"issue":"3\u20134","key":"10.3233\/JIFS-221436_ref1","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1016\/j.mcm.2012.08.001","article-title":"The weighted vertex PI index","volume":"57","author":"Ili\u0107","year":"2013","journal-title":"Mathematical and Computer Modelling"},{"issue":"3","key":"10.3233\/JIFS-221436_ref2","doi-asserted-by":"crossref","first-page":"2150019","DOI":"10.1142\/S1793830921500191","article-title":"Weighted PI index oftensor product and strong product of graphs","volume":"13","author":"Gopika","year":"2020","journal-title":"DiscreteMathematics, Algorithms and Applications"},{"issue":"7","key":"10.3233\/JIFS-221436_ref3","doi-asserted-by":"crossref","first-page":"1603","DOI":"10.1007\/s10910-021-01255-1","article-title":"On graphs preserving PI indexupon edge removal","volume":"59","author":"Indulal","year":"2021","journal-title":"Journal of Mathematical Chemistry"},{"issue":"05","key":"10.3233\/JIFS-221436_ref4","doi-asserted-by":"crossref","first-page":"2150050","DOI":"10.1142\/S1793830921500506","article-title":"Total colorings of circulantgraphs","volume":"13","author":"Geetha","year":"2021","journal-title":"Discrete Mathematics, Algorithms and Applications"},{"issue":"3","key":"10.3233\/JIFS-221436_ref5","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.dam.2011.10.020","article-title":"On some topological indices of thetensor products of graphs","volume":"160","author":"Pattabiraman","year":"2012","journal-title":"Discrete Applied Mathematics"},{"issue":"4","key":"10.3233\/JIFS-221436_ref6","doi-asserted-by":"crossref","first-page":"749","DOI":"10.7151\/dmgt.1647","article-title":"Wiener and vertex PI indices of thestrong product of graphs","volume":"32","author":"Pattabiraman","year":"2012","journal-title":"Discussiones Mathematicae GraphTheory"},{"issue":"10","key":"10.3233\/JIFS-221436_ref7","first-page":"1780","article-title":"Vertex and edge PIindices of Cartesian product graphs","volume":"156","author":"Khalifeh","year":"2008","journal-title":"Discrete AppliedMathematics"},{"issue":"1","key":"10.3233\/JIFS-221436_ref8","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s10910-006-9100-2","article-title":"A method of computing the PIindex of benzenoid hydrocarbons using orthogonal cuts","volume":"42","author":"John","year":"2007","journal-title":"Journalof Mathematical Chemistry"},{"key":"10.3233\/JIFS-221436_ref9","doi-asserted-by":"crossref","unstructured":"Prasanna Poojary, A. Raghavendra and B. Gautham Shenoy, MohammadReza Farahani and Badekara Sooryanarayana, Certain topologicalindices and polynomials for the Isaac graphs, Journal ofDiscrete Mathematical Sciences and Cryptography 24(2) (2021), 511\u2013525.","DOI":"10.1080\/09720529.2021.1896648"},{"issue":"4","key":"10.3233\/JIFS-221436_ref10","doi-asserted-by":"crossref","first-page":"934","DOI":"10.1021\/ci0003092","article-title":"A novel PI index andits applications to QSPR\/QSAR studies","volume":"41","author":"Khadikar","year":"2001","journal-title":"Journal of ChemicalInformation and Computer Sciences"},{"key":"10.3233\/JIFS-221436_ref11","doi-asserted-by":"crossref","first-page":"92","DOI":"10.47443\/dml.2021.s215","article-title":"Padmakar-Ivan index of some types of perfect graphs","volume":"9","author":"Manju","year":"2022","journal-title":"Discrete Mathematics Letters"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-221436","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:43:08Z","timestamp":1777455788000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-221436"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,5]]},"references-count":11,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.3233\/jifs-221436","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,5]]}}}