{"id":"https://openalex.org/W2983217943","doi":"https://doi.org/10.1109/access.2019.2952192","title":"On the Families of Graphs With Unbounded Metric Dimension","display_name":"On the Families of Graphs With Unbounded Metric Dimension","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2983217943","doi":"https://doi.org/10.1109/access.2019.2952192","mag":"2983217943"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2952192","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2952192","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2019.2952192","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101799144","display_name":"Heng Pan","orcid":"https://orcid.org/0000-0001-6602-4505"},"institutions":[{"id":"https://openalex.org/I4210156804","display_name":"First Affiliated Hospital of Zhengzhou University","ror":"https://ror.org/056swr059","country_code":"CN","type":"healthcare","lineage":["https://openalex.org/I4210156804"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Heng Pan","raw_affiliation_strings":["Information Department, First Affiliated Hospital of Zhengzhou University, Zhengzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Information Department, First Affiliated Hospital of Zhengzhou University, Zhengzhou, China","institution_ids":["https://openalex.org/I4210156804"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102763130","display_name":"Murtaza Ali","orcid":null},"institutions":[{"id":"https://openalex.org/I142732210","display_name":"University of Engineering and Technology Lahore","ror":"https://ror.org/0051w2v06","country_code":"PK","type":"education","lineage":["https://openalex.org/I142732210"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Murtaza Ali","raw_affiliation_strings":["Department of Basic sciences & Islamyat, University of Engineering & Technology, Mardan, Mardan, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-0337-1267","affiliations":[{"raw_affiliation_string":"Department of Basic sciences & Islamyat, University of Engineering & Technology, Mardan, Mardan, Pakistan","institution_ids":["https://openalex.org/I142732210"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040600689","display_name":"Gohar Ali","orcid":"https://orcid.org/0000-0002-6466-3992"},"institutions":[{"id":"https://openalex.org/I206573129","display_name":"Islamia College University","ror":"https://ror.org/02p2c1595","country_code":"PK","type":"education","lineage":["https://openalex.org/I206573129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Gohar Ali","raw_affiliation_strings":["Department of Mathematics, Islamia College Peshawar, Peshawar, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-6466-3992","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Islamia College Peshawar, Peshawar, Pakistan","institution_ids":["https://openalex.org/I206573129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113857185","display_name":"Muhammad Tariq Rahim","orcid":null},"institutions":[{"id":"https://openalex.org/I3131573596","display_name":"Abbottabad University of Science and Technology","ror":"https://ror.org/0549hdw45","country_code":"PK","type":"education","lineage":["https://openalex.org/I3131573596"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Tariq Rahim","raw_affiliation_strings":["Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan","institution_ids":["https://openalex.org/I3131573596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101864196","display_name":"Xiaopeng Yang","orcid":"https://orcid.org/0000-0001-9594-1812"},"institutions":[{"id":"https://openalex.org/I4210156804","display_name":"First Affiliated Hospital of Zhengzhou University","ror":"https://ror.org/056swr059","country_code":"CN","type":"healthcare","lineage":["https://openalex.org/I4210156804"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaopeng Yang","raw_affiliation_strings":["Medical Equipment Department, First Affiliated Hospital of Zhengzhou University, Zhengzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Medical Equipment Department, First Affiliated Hospital of Zhengzhou University, Zhengzhou, China","institution_ids":["https://openalex.org/I4210156804"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.7103,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.74200446,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"7","issue":null,"first_page":"165060","last_page":"165064"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/metric-dimension","display_name":"Metric dimension","score":0.9145594239234924},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7234334945678711},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6986405253410339},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6440699100494385},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5327873826026917},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5301122665405273},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47195592522621155},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.20132958889007568},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.15074333548545837}],"concepts":[{"id":"https://openalex.org/C60933471","wikidata":"https://www.wikidata.org/wiki/Q17152964","display_name":"Metric dimension","level":5,"score":0.9145594239234924},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7234334945678711},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6986405253410339},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6440699100494385},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5327873826026917},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5301122665405273},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47195592522621155},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.20132958889007568},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.15074333548545837},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2019.2952192","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2952192","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:45cbd164f3f64b2b94e01c11fa249111","is_oa":true,"landing_page_url":"https://doaj.org/article/45cbd164f3f64b2b94e01c11fa249111","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 7, Pp 165060-165064 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2952192","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2952192","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1886309127","https://openalex.org/W2011039300","https://openalex.org/W2023570253","https://openalex.org/W2026014023","https://openalex.org/W2037298352","https://openalex.org/W2037493128","https://openalex.org/W2108442028","https://openalex.org/W2184012450","https://openalex.org/W2186005361","https://openalex.org/W2811003804","https://openalex.org/W2885319479","https://openalex.org/W2916395413","https://openalex.org/W2916720581","https://openalex.org/W2921947540","https://openalex.org/W4285719527","https://openalex.org/W6686104657"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2561539344","https://openalex.org/W1758702617","https://openalex.org/W2955893777","https://openalex.org/W3133002653","https://openalex.org/W2952616125","https://openalex.org/W3046383293","https://openalex.org/W2912814998","https://openalex.org/W4287702462","https://openalex.org/W52235624"],"abstract_inverted_index":{"A":[0],"family":[1,8],"G":[2],"of":[3,23,33,40,51,60,62],"connected":[4],"graphs":[5,36,53],"is":[6,15],"a":[7,41],"with":[9],"unbounded":[10],"metric":[11,31,49],"dimension":[12,32,50],"if":[13],"dim(G)":[14],"not":[16],"constant":[17],"and":[18,38,43,55],"depends":[19,56],"on":[20,57],"the":[21,30,34,48,58,63],"order":[22],"graph.":[24,64],"In":[25],"this":[26],"paper,":[27],"we":[28],"compute":[29],"splitting":[35],"S(Pn)":[37],"S(Cn)":[39],"path":[42],"cycle.":[44],"We":[45],"prove":[46],"that":[47],"these":[52],"varies":[54],"number":[59],"vertices":[61]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
