{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T05:39:01Z","timestamp":1771306741452,"version":"3.50.1"},"reference-count":31,"publisher":"EDP Sciences","issue":"6","license":[{"start":{"date-parts":[[2023,12,4]],"date-time":"2023-12-04T00:00:00Z","timestamp":1701648000000},"content-version":"vor","delay-in-days":33,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Nil","award":["Nil"],"award-info":[{"award-number":["Nil"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2023,11,1]]},"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:p>In a graph <jats:italic>G<\/jats:italic>, if each node <jats:italic>v<\/jats:italic>\u00a0\u2208\u00a0<jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>)\u00a0\\\u00a0<jats:italic>S<\/jats:italic> is connected to some node in <jats:italic>S<\/jats:italic>, then the set <jats:italic>S<\/jats:italic> of nodes is referred to as a dominating set. The domination number of <jats:italic>G<\/jats:italic> is the minimum cardinality of all dominating sets of <jats:italic>G<\/jats:italic> and is represented by <jats:italic>\u03b3<\/jats:italic>(<jats:italic>G<\/jats:italic>). If a dominating set <jats:italic>S<\/jats:italic> monitors every node in the system under a set of guidelines for power systems monitoring, then the set <jats:italic>S<\/jats:italic> is referred to as a power-dominating set of <jats:italic>G<\/jats:italic>. The power domination number of <jats:italic>G<\/jats:italic> is the least number of vertices of a power dominating set of <jats:italic>G<\/jats:italic>. A generalization of power domination is the <jats:italic>k<\/jats:italic>-power domination in a graph <jats:italic>G<\/jats:italic>. The <jats:italic>k<\/jats:italic>-power domination number of <jats:italic>G<\/jats:italic> is the minimum cardinality of all <jats:italic>k<\/jats:italic>-power dominating sets of <jats:italic>G<\/jats:italic> and is represented by <jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic>,<jats:italic>k<\/jats:italic><\/jats:sub>(G). In this paper, we have obtained the 2-power domination number represented by <jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>p<\/jats:italic>,2<\/jats:sub>(G) for 4-regular Kn\u00f6del graphs and given the lower bound for 5-regular Kn\u00f6del graphs.<\/jats:p>","DOI":"10.1051\/ro\/2023173","type":"journal-article","created":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T19:59:18Z","timestamp":1699041558000},"page":"3157-3168","source":"Crossref","is-referenced-by-count":3,"title":["2-power domination number for Kn\u00f6del graphs and its application in communication networks"],"prefix":"10.1051","volume":"57","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1851-6334","authenticated-orcid":false,"given":"R.","family":"Sundara Rajan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9862-0213","authenticated-orcid":false,"given":"S.","family":"Arulanand","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1922-910X","authenticated-orcid":false,"given":"S.","family":"Prabhu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9721-9505","authenticated-orcid":false,"given":"Indra","family":"Rajasingh","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2023,12,4]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"113038","DOI":"10.1016\/j.disc.2022.113038","volume":"345","author":"Alameda","year":"2022","journal-title":"Discrete Math."},{"key":"R2","doi-asserted-by":"crossref","first-page":"3367","DOI":"10.1051\/ro\/2022150","volume":"56","author":"Aziz","year":"2022","journal-title":"RAIRO:RO"},{"key":"R3","first-page":"17","volume":"74","author":"Balakrishnan","year":"2019","journal-title":"Australas. 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