{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:51:24Z","timestamp":1777704684378,"version":"3.51.4"},"reference-count":41,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2018,11,5]],"date-time":"2018-11-05T00:00:00Z","timestamp":1541376000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2018,12,24]]},"abstract":"<jats:p>\n                    Let\n                    <jats:italic>G<\/jats:italic>\n                    (\n                    <jats:italic>V<\/jats:italic>\n                    ,\n                    <jats:italic>E<\/jats:italic>\n                    ) be a Graph. A set\n                    <jats:italic>W<\/jats:italic>\n                    \u2286\n                    <jats:italic>V<\/jats:italic>\n                    of vertices resolves a graph\n                    <jats:italic>G<\/jats:italic>\n                    if every vertex of\n                    <jats:italic>G<\/jats:italic>\n                    is uniquely determined by its vector of distances to the vertices in\n                    <jats:italic>W<\/jats:italic>\n                    . The metric dimension of\n                    <jats:italic>G<\/jats:italic>\n                    is the minimum cardinality of a resolving set. By imposing different conditions on\n                    <jats:italic>W<\/jats:italic>\n                    we get conditional resolving sets. A resolving set\n                    <jats:italic>W<\/jats:italic>\n                    is said to be an independent resolving set if\n                    <jats:italic>W<\/jats:italic>\n                    contains isolated vertices. Independent resolving number denoted by i\n                    <jats:italic>r<\/jats:italic>\n                    (G) is referred to its cardinality. In this paper we investigate independent resolving number for Titanium dioxide Nanotube.\n                  <\/jats:p>","DOI":"10.3233\/jifs-181314","type":"journal-article","created":{"date-parts":[[2018,11,9]],"date-time":"2018-11-09T15:25:07Z","timestamp":1541777107000},"page":"6421-6425","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":8,"title":["On independent resolving number of\n                    <i>TiO<\/i>\n                    <sub>2<\/sub>\n                    [\n                    <i>m<\/i>\n                    ,\n                    <i>n<\/i>\n                    ] nanotubes"],"prefix":"10.1177","volume":"35","author":[{"given":"S.","family":"Prabhu","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Sri Venkateswara College of Engineering, Sriperumbudur, India"}]},{"given":"T.","family":"Flora","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Sairam Institute of Technology, Chennai, India"}]},{"given":"M.","family":"Arulperumjothi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Loyola College, Chennai, India"}]}],"member":"179","published-online":{"date-parts":[[2018,11,5]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-015-1653-z"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.2006.884015"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(00)00198-0"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/050641867"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.01.003"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-013-1000-3"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2015.03.010"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2017.01.006"},{"key":"e_1_3_1_10_2","volume-title":"Computers and Intractability: A Guide to the Theory of NP-Completeness","author":"Garey M.R.","year":"1979","unstructured":"M.R.Garey and D.S.Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. 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