{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T16:09:38Z","timestamp":1758816578896,"version":"3.41.2"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100001501","name":"University Grants Commission","doi-asserted-by":"publisher","award":["F.510\/3\/DRS-III\/2016(SAP-I)"],"award-info":[{"award-number":["F.510\/3\/DRS-III\/2016(SAP-I)"]}],"id":[{"id":"10.13039\/501100001501","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Karnatak University Dharwad, Karnataka, India","award":["KU\/Sch\/URS\/2017-18\/471 dated 03\/07\/2018"],"award-info":[{"award-number":["KU\/Sch\/URS\/2017-18\/471 dated 03\/07\/2018"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,10]]},"abstract":"<jats:p> Let [Formula: see text] be a graph with vertex set [Formula: see text], and let [Formula: see text] denote the length of a shortest [Formula: see text] path in [Formula: see text]. A set [Formula: see text] is called a connected resolving set of [Formula: see text] if, for any distinct [Formula: see text], there exists a vertex [Formula: see text] such that [Formula: see text], and the subgraph of [Formula: see text] induced by [Formula: see text] is connected. The connected metric dimension, [Formula: see text], of [Formula: see text] is the minimum of the cardinalities over all connected resolving sets of [Formula: see text]. For a graph [Formula: see text] and its complement [Formula: see text], each of order [Formula: see text] and connected, we conjecture that [Formula: see text]; if [Formula: see text] is a tree or a unicyclic graph, we prove the conjecture and characterize graphs achieving equality. <\/jats:p>","DOI":"10.1142\/s1793830921500592","type":"journal-article","created":{"date-parts":[[2020,11,12]],"date-time":"2020-11-12T04:19:35Z","timestamp":1605154775000},"source":"Crossref","is-referenced-by-count":2,"title":["On the connected metric dimension of graphs and their complements"],"prefix":"10.1142","volume":"13","author":[{"given":"Eunjeong","family":"Yi","sequence":"first","affiliation":[{"name":"Texas A&M University at Galveston, Galveston, TX 77553, USA"}]}],"member":"219","published-online":{"date-parts":[[2020,12,7]]},"reference":[{"key":"S1793830921500592BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2018.11.002"},{"volume-title":"Computers and Intractability: A Guide to the Theory of NP-Completeness","year":"1979","author":"Garey M. R.","key":"S1793830921500592BIB002"},{"key":"S1793830921500592BIB003","first-page":"191","volume":"2","author":"Harary F.","year":"1976","journal-title":"Ars Combin."},{"key":"S1793830921500592BIB004","doi-asserted-by":"publisher","DOI":"10.37236\/302"},{"key":"S1793830921500592BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(95)00106-2"},{"key":"S1793830921500592BIB006","doi-asserted-by":"publisher","DOI":"10.2307\/2306658"},{"key":"S1793830921500592BIB007","first-page":"549","volume":"14","author":"Slater P. J.","year":"1975","journal-title":"Congr. Numer."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921500592","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,14]],"date-time":"2021-10-14T03:58:41Z","timestamp":1634183921000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921500592"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,7]]},"references-count":7,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["10.1142\/S1793830921500592"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921500592","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2020,12,7]]},"article-number":"2150059"}}