{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T09:14:12Z","timestamp":1769159652470,"version":"3.49.0"},"reference-count":15,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,6,8]],"date-time":"2018-06-08T00:00:00Z","timestamp":1528416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let G = (V, E) be a connected graph and d(u, v) denote the distance between the vertices u and v in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G and is denoted by dim(G). Let J2n,m be a m-level gear graph obtained by m-level wheel graph W2n,m \u2245 mC2n + k1 by alternatively deleting n spokes of each copy of C2n and J3n be a generalized gear graph obtained by alternately deleting 2n spokes of the wheel graph W3n. In this paper, the metric dimension of certain gear graphs J2n,m and J3n generated by wheel has been computed. Also this study extends the previous result given by Tomescu et al. in 2007.<\/jats:p>","DOI":"10.3390\/sym10060209","type":"journal-article","created":{"date-parts":[[2018,6,8]],"date-time":"2018-06-08T11:19:31Z","timestamp":1528456771000},"page":"209","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Computing the Metric Dimension of Gear Graphs"],"prefix":"10.3390","volume":"10","author":[{"given":"Shahid","family":"Imran","sequence":"first","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Lahore Campus 54000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2607-4847","authenticated-orcid":false,"given":"Muhammad Kamran","family":"Siddiqui","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Sahiwal Campus 57000, Pakistan"},{"name":"Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, United Arab Emirates"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2827-0462","authenticated-orcid":false,"given":"Muhammad","family":"Imran","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, United Arab Emirates"},{"name":"Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad 44000, Pakistan"}]},{"given":"Muhammad","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Lahore Campus 54000, Pakistan"}]},{"given":"Hafiz Muhammad","family":"Bilal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Lahore Campus 54000, Pakistan"}]},{"given":"Imran Zulfiqar","family":"Cheema","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Lahore Campus 54000, Pakistan"}]},{"given":"Ali","family":"Tabraiz","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of Central Punjab, Lahore 54000, Pakistan"}]},{"given":"Zeeshan","family":"Saleem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Lahore, Old Campus Lahore 54000, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,8]]},"reference":[{"key":"ref_1","first-page":"371","article-title":"On the metric dimension of the jahangir graph","volume":"50","author":"Tomescu","year":"2007","journal-title":"Bull. 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Res."},{"key":"ref_15","unstructured":"Bras, R.L., Gomes, C.P., and Selman, B. (2013, January 3\u20139). Double-wheel graphs are graceful. Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence, Beijing, China."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/6\/209\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:07:57Z","timestamp":1760195277000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/6\/209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,8]]},"references-count":15,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2018,6]]}},"alternative-id":["sym10060209"],"URL":"https:\/\/doi.org\/10.3390\/sym10060209","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,8]]}}}