{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T03:57:17Z","timestamp":1771559837259,"version":"3.50.1"},"reference-count":44,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,4,5]],"date-time":"2021-04-05T00:00:00Z","timestamp":1617580800000},"content-version":"vor","delay-in-days":94,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Anhui Natural Science Research Project","award":["KJ2020A0696"],"award-info":[{"award-number":["KJ2020A0696"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>The number of edges in a shortest walk (without repetition of vertices) from one vertex to another vertex of a connected graph <jats:italic>G<\/jats:italic> is known as the distance between them. For a vertex <jats:italic>x<\/jats:italic> and an edge <jats:italic>e<\/jats:italic> = <jats:italic>a<\/jats:italic><jats:italic>b<\/jats:italic> in <jats:italic>G<\/jats:italic>, the minimum number from distances of <jats:italic>x<\/jats:italic> with <jats:italic>a<\/jats:italic> and <jats:italic>b<\/jats:italic> is said to be the distance between <jats:italic>x<\/jats:italic> and <jats:italic>e<\/jats:italic>. A vertex <jats:italic>x<\/jats:italic> is said to distinguish (resolves) two distinct edges <jats:italic>e<\/jats:italic><jats:sub>1<\/jats:sub> and <jats:italic>e<\/jats:italic><jats:sub>2<\/jats:sub> if the distance between <jats:italic>x<\/jats:italic> and <jats:italic>e<\/jats:italic><jats:sub>1<\/jats:sub> is different from the distance between <jats:italic>x<\/jats:italic> and <jats:italic>e<\/jats:italic><jats:sub>2<\/jats:sub>. A set <jats:italic>X<\/jats:italic> of vertices in a connected graph <jats:italic>G<\/jats:italic> is an edge metric generator for <jats:italic>G<\/jats:italic> if every two edges of <jats:italic>G<\/jats:italic> are distinguished by some vertex in <jats:italic>X<\/jats:italic>. The number of vertices in such a smallest set <jats:italic>X<\/jats:italic> is known as the edge metric dimension of <jats:italic>G<\/jats:italic>. In this article, we solve the edge metric dimension problem for certain classes of planar graphs.<\/jats:p>","DOI":"10.1155\/2021\/5599274","type":"journal-article","created":{"date-parts":[[2021,4,5]],"date-time":"2021-04-05T19:50:07Z","timestamp":1617652207000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Classes of Planar Graphs with Constant Edge Metric Dimension"],"prefix":"10.1155","volume":"2021","author":[{"given":"Changcheng","family":"Wei","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1725-4202","authenticated-orcid":false,"given":"Muhammad","family":"Salman","sequence":"additional","affiliation":[]},{"given":"Syed","family":"Shahzaib","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2783-6337","authenticated-orcid":false,"given":"Masood Ur","family":"Rehman","sequence":"additional","affiliation":[]},{"given":"Juanyan","family":"Fang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,4,5]]},"reference":[{"key":"e_1_2_8_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0166-218x(00)00198-0"},{"key":"e_1_2_8_2_2","first-page":"191","article-title":"On the metric dimension of a graph","volume":"2","author":"Harary F.","year":"1976","journal-title":"Ars Combinatoria"},{"key":"e_1_2_8_3_2","first-page":"549","article-title":"Leaves of trees","volume":"14","author":"Slater P. J.","year":"1975","journal-title":"Congressus Numerantium"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/jsac.2006.884015"},{"key":"e_1_2_8_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf02579188"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218x(95)00106-2"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1963.11992174"},{"key":"e_1_2_8_8_2","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1030.0070"},{"key":"e_1_2_8_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.05.039"},{"key":"e_1_2_8_10_2","doi-asserted-by":"publisher","DOI":"10.21136\/mb.2003.133935"},{"key":"e_1_2_8_11_2","doi-asserted-by":"publisher","DOI":"10.1137\/050641867"},{"key":"e_1_2_8_12_2","doi-asserted-by":"publisher","DOI":"10.21136\/mb.2003.134003"},{"key":"e_1_2_8_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-014-9896-2"},{"key":"e_1_2_8_14_2","first-page":"2829","article-title":"The k\u2212metric dimension of a grpah","volume":"9","author":"Estrada-Moreno A.","year":"2015","journal-title":"Applied Mathematics & Information Sciences"},{"key":"e_1_2_8_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2019.02.013"},{"key":"e_1_2_8_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2017.07.027"},{"key":"e_1_2_8_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2018.05.052"},{"key":"e_1_2_8_18_2","doi-asserted-by":"publisher","DOI":"10.21136\/mb.2010.140702"},{"key":"e_1_2_8_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.endm.2014.08.032"},{"key":"e_1_2_8_20_2","first-page":"3","article-title":"Connected resolving sets in graphs","volume":"68","author":"Saenpholphat V.","year":"2003","journal-title":"Ars Combinatoria"},{"key":"e_1_2_8_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2018.04.010"},{"key":"e_1_2_8_22_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2020286"},{"key":"e_1_2_8_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00025-019-1105-9"},{"key":"e_1_2_8_24_2","first-page":"714","article-title":"Computation of edge metric dimension of barcycentric subdivision of cayley graphs","author":"Mufti Z.","year":"2020","journal-title":"Italian Journal of Pure and Applied Mathematics"},{"key":"e_1_2_8_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40840-019-00816-7"},{"key":"e_1_2_8_26_2","doi-asserted-by":"publisher","DOI":"10.3390\/math6110243"},{"key":"e_1_2_8_27_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10878-019-00472-4"},{"key":"e_1_2_8_28_2","first-page":"143","article-title":"Edge metric dimension of graphs","volume":"147","author":"Nasir R.","year":"2018","journal-title":"Ars Combinatoria"},{"key":"e_1_2_8_29_2","doi-asserted-by":"publisher","DOI":"10.1216\/rmj.2020.50.1175"},{"key":"e_1_2_8_30_2","doi-asserted-by":"publisher","DOI":"10.2478\/auom-2020-0032"},{"key":"e_1_2_8_31_2","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/1180\/1\/012005"},{"key":"e_1_2_8_32_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-020-01669-x"},{"key":"e_1_2_8_33_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2021.126076"},{"key":"e_1_2_8_34_2","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/1543\/1\/012009"},{"key":"e_1_2_8_35_2","first-page":"24","article-title":"Labellings of two classes of convex polytopes","volume":"34","author":"Baca M.","year":"1988","journal-title":"Utilitas Mathematica"},{"key":"e_1_2_8_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2010.08.090"},{"key":"e_1_2_8_37_2","doi-asserted-by":"publisher","DOI":"10.1109\/tc.1981.1675777"},{"key":"e_1_2_8_38_2","doi-asserted-by":"publisher","DOI":"10.1090\/s0002-9904-1950-09407-5"},{"key":"e_1_2_8_39_2","first-page":"61","article-title":"Labeling of chordal rings","volume":"90","author":"Javaid I.","year":"2013","journal-title":"Utilitas Mathematica"},{"key":"e_1_2_8_40_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5"},{"key":"e_1_2_8_41_2","doi-asserted-by":"publisher","DOI":"10.1109\/access.2020.3025018"},{"key":"e_1_2_8_42_2","doi-asserted-by":"publisher","DOI":"10.1109\/access.2020.2990109"},{"key":"e_1_2_8_43_2","doi-asserted-by":"publisher","DOI":"10.1109\/access.2020.2991685"},{"key":"e_1_2_8_44_2","first-page":"801","article-title":"The edge metric dimension of Cayley graphs \u0393Zn\u2295Z2 and its barycentric subdivisions","volume":"24","author":"Raza Z.","year":"2019","journal-title":"Nonlinear Functional Analysis and Applications"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/5599274.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/5599274.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/5599274","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T22:31:42Z","timestamp":1723242702000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/5599274"}},"subtitle":[],"editor":[{"given":"M. Irfan","family":"Uddin","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":44,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/5599274"],"URL":"https:\/\/doi.org\/10.1155\/2021\/5599274","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2021-02-26","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-03-22","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-04-05","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"5599274"}}