{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:38:18Z","timestamp":1760146698982,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T00:00:00Z","timestamp":1732752000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The field of indices has been explored and advanced by various researchers for different purposes. One purpose is the optimization of indices in various problems. In this work, the general power-sum connectivity index is considered. The general power-sum connectivity index was investigated for k-generalized quasi-trees where optimal graphs were found. Further, in this work, we extend the idea of optimization to families of graphs, including uni-cyclic graphs, bi-cyclic graphs and trees. The optimization is carried out by means of operations named as Operation A, B, C and D. The first two operations increase the value of the general power-sum connectivity index, while the last two work opposite to Operations A and B. These operations are explained by means of diagrams, where one can easily obtain their working procedures.<\/jats:p>","DOI":"10.3390\/axioms13120840","type":"journal-article","created":{"date-parts":[[2024,12,4]],"date-time":"2024-12-04T10:07:10Z","timestamp":1733306830000},"page":"840","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimization of General Power-Sum Connectivity Index in Uni-Cyclic Graphs, Bi-Cyclic Graphs and Trees by Means of Operations"],"prefix":"10.3390","volume":"13","author":[{"given":"Muhammad Yasin","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Islamia College Peshawar, Peshawar 25120, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gohar","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Islamia College Peshawar, Peshawar 25120, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8042-1806","authenticated-orcid":false,"given":"Ioan-Lucian","family":"Popa","sequence":"additional","affiliation":[{"name":"Department of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, Romania"},{"name":"Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,28]]},"reference":[{"key":"ref_1","unstructured":"Rosen, K.H. 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