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An <jats:italic>r<\/jats:italic>-locating-dominating set (<jats:italic>r<\/jats:italic>-locating-total dominating set) of <jats:italic>G<\/jats:italic> is an <jats:italic>r<\/jats:italic>-dominating set (<jats:italic>r<\/jats:italic>-total dominating set) <jats:italic>S<\/jats:italic> of <jats:italic>G<\/jats:italic> for which <jats:italic>N<jats:sub>r<\/jats:sub><\/jats:italic>(<jats:italic>u<\/jats:italic>) <jats:italic>\u2229<\/jats:italic> <jats:italic>S<\/jats:italic> is different from <jats:italic>N<jats:sub>r<\/jats:sub><\/jats:italic>(<jats:italic>v<\/jats:italic>) <jats:italic>\u2229<\/jats:italic> <jats:italic>S<\/jats:italic> for all <jats:italic>u<\/jats:italic> and <jats:italic>v<\/jats:italic> not in <jats:italic>S<\/jats:italic>. This paper presents an extension of the locating-total dominating set of <jats:italic>G<\/jats:italic>. Further, we establish a lower bound on <jats:italic>r<\/jats:italic>-locating-dominating set and <jats:italic>r<\/jats:italic>-locating-total dominating set for <jats:italic>k<\/jats:italic>-regular graphs, as well as demonstrate that <jats:italic>r<\/jats:italic>-locating-total dominating set is an NP-complete problem. Furthermore, the <jats:italic>r<\/jats:italic>-locating-dominating set and <jats:italic>r<\/jats:italic>-locating-total dominating set problems are discussed for some standard graphs.<\/jats:p>","DOI":"10.1051\/ro\/2024123","type":"journal-article","created":{"date-parts":[[2024,6,6]],"date-time":"2024-06-06T19:00:52Z","timestamp":1717700452000},"page":"4889-4904","source":"Crossref","is-referenced-by-count":0,"title":["An extension of locating-total domination problem and its complexity"],"prefix":"10.1051","volume":"58","author":[{"given":"N.","family":"Eswar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7878-1578","authenticated-orcid":false,"given":"R.","family":"Jayagopal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2024,11,21]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.endm.2015.07.016","volume":"50","author":"Argiroffo","year":"2015","journal-title":"Electron. 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