{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:02:32Z","timestamp":1753887752011,"version":"3.41.2"},"reference-count":11,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T00:00:00Z","timestamp":1629676800000},"content-version":"vor","delay-in-days":234,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005357","name":"Slovak Research and Development Agency","doi-asserted-by":"crossref","award":["APVV-19-0153","VEGA 1\/0233\/18"],"award-info":[{"award-number":["APVV-19-0153","VEGA 1\/0233\/18"]}],"id":[{"id":"10.13039\/501100005357","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>In this work, we introduce a new topological index called a general power sum\u2010connectivity index and we discuss this graph invariant for some classes of extremal graphs. This index is defined by , where <jats:italic>d<\/jats:italic>(<jats:italic>u<\/jats:italic>) and <jats:italic>d<\/jats:italic>(<jats:italic>v<\/jats:italic>) represent the degree of vertices <jats:italic>u<\/jats:italic> and <jats:italic>v<\/jats:italic>, respectively, and <jats:italic>\u03b1<\/jats:italic> \u2265 1. A connected graph <jats:italic>G<\/jats:italic> is called a <jats:italic>k<\/jats:italic>\u2010generalized quasi\u2010tree if there exists a subset <jats:italic>V<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub> \u2282 <jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>) of cardinality <jats:italic>k<\/jats:italic> such that the graph <jats:italic>G<\/jats:italic> \u2212 <jats:italic>V<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub> is a tree but for any subset <jats:italic>V<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic>\u22121<\/jats:sub> \u2282 <jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>) of cardinality <jats:italic>k<\/jats:italic> \u2212 1, the graph <jats:italic>G<\/jats:italic> \u2212 <jats:italic>V<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic>\u22121<\/jats:sub> is not a tree. In this work, we find a sharp lower and some sharp upper bounds for this new sum\u2010connectivity index.<\/jats:p>","DOI":"10.1155\/2021\/6623277","type":"journal-article","created":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T18:10:07Z","timestamp":1629742207000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Investigation of General Power Sum\u2010Connectivity Index for Some Classes of Extremal Graphs"],"prefix":"10.1155","volume":"2021","author":[{"given":"Rui","family":"Cheng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6466-3992","authenticated-orcid":false,"given":"Gohar","family":"Ali","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gul","family":"Rahmat","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Yasin","family":"Khan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8432-9836","authenticated-orcid":false,"given":"Andrea","family":"Semanicova-Fenovcikova","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9620-7692","authenticated-orcid":false,"given":"Jia-Bao","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,8,23]]},"reference":[{"key":"e_1_2_7_1_2","first-page":"101","article-title":"Extremal k-generalized quasi trees for general sum-connectivity index","volume":"82","author":"Jamil M. 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