{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:24:44Z","timestamp":1753885484830,"version":"3.41.2"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"name":"the NSF of China","award":["11971146"],"award-info":[{"award-number":["11971146"]}]},{"name":"the NSF of Hebei Province","award":["A2017403010"],"award-info":[{"award-number":["A2017403010"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2024,5]]},"abstract":"<jats:p> Let [Formula: see text] be a connected graph where [Formula: see text] is the set of vertices of [Formula: see text] and [Formula: see text] is the set of edges of [Formula: see text]. The distance from the vertex [Formula: see text] to the edge\u00a0[Formula: see text] is given by [Formula: see text]. A subset [Formula: see text] is called an edge metric generator for [Formula: see text] if for every two distinct edges [Formula: see text], there exists a vertex [Formula: see text] such that [Formula: see text]. The edge metric generator with the minimum number of vertices is called an edge metric basis for [Formula: see text] and the cardinality of the edge metric basis is called the edge metric dimension denoted by [Formula: see text]. A subset [Formula: see text] is called a mixed metric generator for [Formula: see text] if for every two distinct elements [Formula: see text], there exists a vertex [Formula: see text] such that [Formula: see text]. A mixed metric generator containing a minimum number of vertices is called a mixed metric basis for [Formula: see text] and the cardinality of a mixed metric basis is called the mixed metric dimension denoted by [Formula: see text]. In this paper, we study the edge metric dimension and the mixed metric dimension of a plane graph\u00a0[Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830923500398","type":"journal-article","created":{"date-parts":[[2023,4,30]],"date-time":"2023-04-30T04:28:40Z","timestamp":1682828920000},"source":"Crossref","is-referenced-by-count":0,"title":["Edge metric dimension and mixed metric dimension of a plane graph Tn"],"prefix":"10.1142","volume":"16","author":[{"given":"Huige","family":"Shen","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, P. R. China"}]},{"given":"Jing","family":"Qu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Science, Hebei GEO University, Shijiazhuang 050031, P. R. China"}]},{"given":"Na","family":"Kang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Science, Hebei GEO University, Shijiazhuang 050031, P. R. 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