{"id":"https://openalex.org/W3151177646","doi":"https://doi.org/10.1155/2021/5599274","title":"Classes of Planar Graphs with Constant Edge Metric Dimension","display_name":"Classes of Planar Graphs with Constant Edge Metric Dimension","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3151177646","doi":"https://doi.org/10.1155/2021/5599274","mag":"3151177646"},"language":"en","primary_location":{"id":"doi:10.1155/2021/5599274","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/5599274","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/5599274.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2021/5599274.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028160847","display_name":"Changcheng Wei","orcid":"https://orcid.org/0000-0001-9985-8338"},"institutions":[{"id":"https://openalex.org/I4210159152","display_name":"Tongling University","ror":"https://ror.org/04kqvjg13","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210159152"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changcheng Wei","raw_affiliation_strings":["Institute of Mathematics and Computer Science, Tongling College, Tongling 244000, China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Computer Science, Tongling College, Tongling 244000, China","institution_ids":["https://openalex.org/I4210159152"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084504594","display_name":"Muhammad Salman","orcid":"https://orcid.org/0000-0003-1725-4202"},"institutions":[{"id":"https://openalex.org/I174731842","display_name":"Islamia University of Bahawalpur","ror":"https://ror.org/002rc4w13","country_code":"PK","type":"education","lineage":["https://openalex.org/I174731842"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Salman","raw_affiliation_strings":["Department of Mathematics,","Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics,","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan","institution_ids":["https://openalex.org/I174731842"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047686394","display_name":"Syed Shahzaib","orcid":null},"institutions":[{"id":"https://openalex.org/I174731842","display_name":"Islamia University of Bahawalpur","ror":"https://ror.org/002rc4w13","country_code":"PK","type":"education","lineage":["https://openalex.org/I174731842"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Syed Shahzaib","raw_affiliation_strings":["Department of Mathematics,","Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics,","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan","institution_ids":["https://openalex.org/I174731842"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100784102","display_name":"Masood Ur Rehman","orcid":"https://orcid.org/0000-0003-2783-6337"},"institutions":[{"id":"https://openalex.org/I4210156098","display_name":"Balochistan University of Engineering and Technology","ror":"https://ror.org/041qsth84","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210156098"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Masood Ur Rehman","raw_affiliation_strings":["Department of Basic Sciences, Balochistan University of Engineering and Technology Khuzdar, Khuzdar 89100, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, Balochistan University of Engineering and Technology Khuzdar, Khuzdar 89100, Pakistan","institution_ids":["https://openalex.org/I4210156098"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037163041","display_name":"Juanyan Fang","orcid":"https://orcid.org/0000-0001-5877-594X"},"institutions":[{"id":"https://openalex.org/I4210159152","display_name":"Tongling University","ror":"https://ror.org/04kqvjg13","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210159152"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Juanyan Fang","raw_affiliation_strings":["Institute of Mathematics and Computer Science, Tongling College, Tongling 244000, China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Computer Science, Tongling College, Tongling 244000, China","institution_ids":["https://openalex.org/I4210159152"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100784102"],"corresponding_institution_ids":["https://openalex.org/I4210156098"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":1.0598,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.79997215,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2021","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5429112911224365},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.500556468963623},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4919757544994354},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4189060628414154},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3330431580543518}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5429112911224365},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.500556468963623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4919757544994354},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4189060628414154},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3330431580543518}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2021/5599274","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/5599274","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/5599274.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:5599274","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2021/5599274.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:667f53520401433aa5b3323acc9c67c6","is_oa":true,"landing_page_url":"https://doaj.org/article/667f53520401433aa5b3323acc9c67c6","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2021 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2021/5599274","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/5599274","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/5599274.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3151177646.pdf","grobid_xml":"https://content.openalex.org/works/W3151177646.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W66989490","https://openalex.org/W1973911938","https://openalex.org/W1974558557","https://openalex.org/W2026014023","https://openalex.org/W2037298352","https://openalex.org/W2059749917","https://openalex.org/W2065234962","https://openalex.org/W2079580449","https://openalex.org/W2083763715","https://openalex.org/W2103905945","https://openalex.org/W2105232761","https://openalex.org/W2108442028","https://openalex.org/W2138978865","https://openalex.org/W2255753884","https://openalex.org/W2324588684","https://openalex.org/W2565824123","https://openalex.org/W2592828425","https://openalex.org/W2751981098","https://openalex.org/W2802116907","https://openalex.org/W2900101803","https://openalex.org/W2917237471","https://openalex.org/W2923839354","https://openalex.org/W2963118757","https://openalex.org/W2966255984","https://openalex.org/W2978678889","https://openalex.org/W2982597716","https://openalex.org/W2995345885","https://openalex.org/W3018313712","https://openalex.org/W3021044933","https://openalex.org/W3024123740","https://openalex.org/W3031679203","https://openalex.org/W3089126889","https://openalex.org/W3090606071","https://openalex.org/W3100731361","https://openalex.org/W3103096210","https://openalex.org/W3118519976","https://openalex.org/W3132124968","https://openalex.org/W4232896595","https://openalex.org/W4236316415","https://openalex.org/W4390770442","https://openalex.org/W6602715938","https://openalex.org/W6743836197"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885","https://openalex.org/W3111310291"],"abstract_inverted_index":{"The":[0,132],"number":[1,46,133],"of":[2,10,18,49,104,122,134,149,165],"edges":[3,76,121],"in":[4,41,106,129,136],"a":[5,19,31,39,52,107,138],"shortest":[6],"walk":[7],"(without":[8],"repetition":[9],"vertices)":[11],"from":[12,47,92],"one":[13],"vertex":[14,17,32,67,128],"to":[15,57,71],"another":[16],"connected":[20,108],"graph":[21,109],"G":[22,42,110,117,123,150],"is":[23,55,69,90,111,142],"known":[24,143],"as":[25,144],"the":[26,44,59,83,93,145,157],"distance":[27,60,84,94],"between":[28,61,85,95],"them.":[29],"For":[30],"x":[33,50,62,68,86,96],"and":[34,53,63,79,87,97],"an":[35,112],"edge":[36,113,146,158],"e":[37,64,77,80,88,98],"=":[38],"b":[40,54],",":[43],"minimum":[45],"distances":[48],"with":[51],"said":[56,70],"be":[58],".":[65,100,131,151],"A":[66,101],"distinguish":[72],"(resolves)":[73],"two":[74,120],"distinct":[75],"1":[78,89],"2":[81,99],"if":[82,118],"different":[91],"set":[102,140],"X":[103,130,141],"vertices":[105,135],"metric":[114,147,159],"generator":[115],"for":[116,162],"every":[119],"are":[124],"distinguished":[125],"by":[126],"some":[127],"such":[137],"smallest":[139],"dimension":[148,160],"In":[152],"this":[153],"article,":[154],"we":[155],"solve":[156],"problem":[161],"certain":[163],"classes":[164],"planar":[166],"graphs.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}