{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T02:07:17Z","timestamp":1773022037801,"version":"3.50.1"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,4]]},"abstract":"<jats:p>A set [Formula: see text] is called a resolving set, if for each pair of distinct vertices [Formula: see text] there exists [Formula: see text] such that [Formula: see text], where [Formula: see text] is the distance between vertices [Formula: see text] and [Formula: see text]. The cardinality of a minimum resolving set for [Formula: see text] is called the metric dimension of [Formula: see text] and is denoted by [Formula: see text]. A [Formula: see text]-tree is a chordal graph all of whose maximal cliques are the same size [Formula: see text] and all of whose minimal clique separators are also all the same size [Formula: see text]. A [Formula: see text]-path is a [Formula: see text]-tree with maximum degree [Formula: see text], where for each integer [Formula: see text], [Formula: see text], there exists a unique pair of vertices, [Formula: see text] and [Formula: see text], such that [Formula: see text]. In this paper, we prove that if [Formula: see text] is a [Formula: see text]-path, then [Formula: see text]. Moreover, we provide a characterization of all [Formula: see text]-trees with metric dimension two.<\/jats:p>","DOI":"10.1142\/s1793830917500276","type":"journal-article","created":{"date-parts":[[2017,2,17]],"date-time":"2017-02-17T08:08:26Z","timestamp":1487318906000},"page":"1750027","source":"Crossref","is-referenced-by-count":7,"title":["A characterization of some graphs with metric dimension two"],"prefix":"10.1142","volume":"09","author":[{"given":"Ali","family":"Behtoei","sequence":"first","affiliation":[{"name":"Department of Mathematics, Imam Khomeini International University, 34149-16818, Qazvin, Iran"}]},{"given":"Akbar","family":"Davoodi","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran"}]},{"given":"Mohsen","family":"Jannesari","sequence":"additional","affiliation":[{"name":"University of Shahreza, 86149-56841, Shahreza, Iran"}]},{"given":"Behnaz","family":"Omoomi","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran"}]}],"member":"219","published-online":{"date-parts":[[2017,4,13]]},"reference":[{"key":"S1793830917500276BIB001","doi-asserted-by":"publisher","DOI":"10.1109\/JSAC.2006.884015"},{"key":"S1793830917500276BIB003","doi-asserted-by":"publisher","DOI":"10.1137\/050641867"},{"key":"S1793830917500276BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(00)00198-0"},{"key":"S1793830917500276BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(92)90041-D"},{"key":"S1793830917500276BIB006","first-page":"191","volume":"2","author":"Harary F.","year":"1976","journal-title":"Ars Combin."},{"issue":"1","key":"S1793830917500276BIB007","doi-asserted-by":"crossref","first-page":"1","DOI":"10.21136\/MB.2014.143632","volume":"139","author":"Janessari M.","year":"2014","journal-title":"Math. Bohem."},{"key":"S1793830917500276BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(95)00106-2"},{"key":"S1793830917500276BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/0734-189X(84)90051-3"},{"key":"S1793830917500276BIB010","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1030.0070"},{"key":"S1793830917500276BIB011","first-page":"549","volume":"14","author":"Slater P. J.","year":"1975","journal-title":"Congr. Numer."},{"key":"S1793830917500276BIB012","first-page":"621","volume":"36","author":"Sudhakara G.","year":"2009","journal-title":"World Acad. Sci. Eng. Technol."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830917500276","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,2]],"date-time":"2020-10-02T16:16:34Z","timestamp":1601655394000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830917500276"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4]]},"references-count":11,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2017,4,13]]},"published-print":{"date-parts":[[2017,4]]}},"alternative-id":["10.1142\/S1793830917500276"],"URL":"https:\/\/doi.org\/10.1142\/s1793830917500276","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4]]}}}