{"id":"https://openalex.org/W3094039970","doi":"https://doi.org/10.1109/access.2020.3030713","title":"On Mixed Metric Dimension of Some Path Related Graphs","display_name":"On Mixed Metric Dimension of Some Path Related Graphs","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3094039970","doi":"https://doi.org/10.1109/access.2020.3030713","mag":"3094039970"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.3030713","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3030713","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09222153.pdf","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://ieeexplore.ieee.org/ielx7/6287639/8948470/09222153.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050403373","display_name":"Hassan Raza","orcid":"https://orcid.org/0000-0002-1477-3608"},"institutions":[{"id":"https://openalex.org/I148128674","display_name":"University of Shanghai for Science and Technology","ror":"https://ror.org/00ay9v204","country_code":"CN","type":"education","lineage":["https://openalex.org/I148128674"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hassan Raza","raw_affiliation_strings":["Business School, University of Shanghai for Science and Technology, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-1477-3608","affiliations":[{"raw_affiliation_string":"Business School, University of Shanghai for Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I148128674"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018213183","display_name":"Ying Ji","orcid":"https://orcid.org/0000-0002-2985-6449"},"institutions":[{"id":"https://openalex.org/I148128674","display_name":"University of Shanghai for Science and Technology","ror":"https://ror.org/00ay9v204","country_code":"CN","type":"education","lineage":["https://openalex.org/I148128674"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ying Ji","raw_affiliation_strings":["Business School, University of Shanghai for Science and Technology, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-2985-6449","affiliations":[{"raw_affiliation_string":"Business School, University of Shanghai for Science and Technology, Shanghai, China","institution_ids":["https://openalex.org/I148128674"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055101551","display_name":"Shaojian Qu","orcid":"https://orcid.org/0000-0002-4746-270X"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN","SG"],"is_corresponding":false,"raw_author_name":"Shaojian Qu","raw_affiliation_strings":["Management Engineering School, University of Nanjing for Information Science and Technology, Nanjing, China","Logistic Institute-Asia Pacific, National University of Singapore, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-4746-270X","affiliations":[{"raw_affiliation_string":"Management Engineering School, University of Nanjing for Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]},{"raw_affiliation_string":"Logistic Institute-Asia Pacific, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"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":1.7957,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.88630435,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"8","issue":null,"first_page":"188146","last_page":"188153"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998999834060669,"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":0.9998999834060669,"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":0.7085076570510864},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6519854664802551},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.555336058139801},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45339256525039673},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.45014387369155884},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43743669986724854},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28581327199935913},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.22959357500076294},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.17192867398262024},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.1023927628993988},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.0749674141407013},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.05970063805580139}],"concepts":[{"id":"https://openalex.org/C60933471","wikidata":"https://www.wikidata.org/wiki/Q17152964","display_name":"Metric dimension","level":5,"score":0.7085076570510864},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6519854664802551},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.555336058139801},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45339256525039673},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.45014387369155884},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43743669986724854},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28581327199935913},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.22959357500076294},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.17192867398262024},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.1023927628993988},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0749674141407013},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.05970063805580139},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2020.3030713","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3030713","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09222153.pdf","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:e7f5c581aea740edb640d72f9ff6ba79","is_oa":true,"landing_page_url":"https://doaj.org/article/e7f5c581aea740edb640d72f9ff6ba79","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 8, Pp 188146-188153 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2020.3030713","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3030713","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09222153.pdf","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":[{"id":"https://openalex.org/G3420362070","display_name":null,"funder_award_id":"1020303302","funder_id":"https://openalex.org/F4320324854","funder_display_name":"University of Shanghai for Science and Technology"},{"id":"https://openalex.org/G950439790","display_name":"\u591a\u76ee\u6807\u9c81\u68d2\u51f8\u89c4\u5212\u95ee\u9898\uff1a\u7406\u8bba\u3001\u7b97\u6cd5\u548c\u5e94\u7528\u7814\u7a76","funder_award_id":"71571055","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324854","display_name":"University of Shanghai for Science and Technology","ror":"https://ror.org/00ay9v204"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3094039970.pdf","grobid_xml":"https://content.openalex.org/works/W3094039970.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W2026014023","https://openalex.org/W2037298352","https://openalex.org/W2074389465","https://openalex.org/W2771087721","https://openalex.org/W2802116907","https://openalex.org/W2806894573","https://openalex.org/W2811210202","https://openalex.org/W2899421048","https://openalex.org/W2900101803","https://openalex.org/W2903472770","https://openalex.org/W2952434773","https://openalex.org/W2963118757","https://openalex.org/W2970222247","https://openalex.org/W2983217943","https://openalex.org/W2997798549","https://openalex.org/W3002907355","https://openalex.org/W3018313712","https://openalex.org/W3024123740","https://openalex.org/W3041566457","https://openalex.org/W3046213918","https://openalex.org/W3186748763","https://openalex.org/W4242242027","https://openalex.org/W6781072551"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2561539344","https://openalex.org/W2142036596","https://openalex.org/W2933449636","https://openalex.org/W3133002653"],"abstract_inverted_index":{"A":[0,23],"vertex":[1,49,60],"k":[2],"\u2208":[3,13],"VG":[4,14],"determined":[5,46],"two":[6,39],"elements":[7,41,57],"(vertices":[8,42],"or":[9,43],"edges)":[10,44],"1,":[11],"m":[12],"U":[15],"EG,":[16],"if":[17,38],"dG(k,":[18,21],"1)":[19],"=6":[20],"m).":[22],"setRm":[24],"of":[25,51,56,62,81,96,102,108,115,124,144,148],"vertices":[26],"in":[27,58],"a":[28,32,97,103,109,116,149],"graph":[29,101,107,114,147],"G":[30],"is":[31,64,86],"mixed":[33,67,78,130],"metric":[34,68,79,131,142],"generator":[35],"for":[36,140],"G,":[37],"distinct":[40],"are":[45,92],"by":[47],"some":[48,82],"set":[50,61],"Rm.":[52],"The":[53],"least":[54],"number":[55],"the":[59,77,94,105,141,145],"Rm":[63],"known":[65],"as":[66,72],"dimension,":[69,132],"and":[70,112,128],"denoted":[71],"dimm(G).":[73],"In":[74],"this":[75],"article,":[76],"dimension":[80,143],"path":[83,89,110,117,150],"related":[84,90],"graphs":[85,91,125],"obtained.":[87],"Those":[88],"P2n":[93],"square":[95],"path,":[98,104],"T(Pn)":[99],"total":[100],"middle":[106],"M(Pn),":[111],"splitting":[113,146],"S(Pn).":[118,151],"We":[119,134],"proved":[120],"that":[121],"these":[122],"families":[123],"have":[126],"constant":[127],"unbounded":[129],"respectively.":[133],"further":[135],"presented":[136],"an":[137],"improved":[138],"result":[139]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2020-10-29T00:00:00"}