{"id":"https://openalex.org/W4417311726","doi":"https://doi.org/10.1007/s40314-025-03548-6","title":"Characterization of graphs with rank $$2v(G)-2\\alpha (G)-2c(G)+1$$","display_name":"Characterization of graphs with rank $$2v(G)-2\\alpha (G)-2c(G)+1$$","publication_year":2025,"publication_date":"2025-12-15","ids":{"openalex":"https://openalex.org/W4417311726","doi":"https://doi.org/10.1007/s40314-025-03548-6"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-025-03548-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-025-03548-6","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100750900","display_name":"Feng Liu","orcid":"https://orcid.org/0000-0002-6903-6840"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng Liu","raw_affiliation_strings":["School of Mathematics Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071021268","display_name":"Qi Wu","orcid":"https://orcid.org/0000-0001-8642-0783"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qi Wu","raw_affiliation_strings":["School of Mathematical Sciences, Key Laboratory of Mathematics and Engineering Applications (Ministry of Education) and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Key Laboratory of Mathematics and Engineering Applications (Ministry of Education) and Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, China","institution_ids":["https://openalex.org/I66867065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071021268"],"corresponding_institution_ids":["https://openalex.org/I66867065"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.45487574,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.35269999504089355,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.35269999504089355,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10849","display_name":"Finite Group Theory Research","score":0.2721000015735626,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11476","display_name":"Graph theory and applications","score":0.09549999982118607,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6934999823570251},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.6134999990463257},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5385000109672546},{"id":"https://openalex.org/keywords/metric-dimension","display_name":"Metric dimension","score":0.3919999897480011},{"id":"https://openalex.org/keywords/cyclomatic-complexity","display_name":"Cyclomatic complexity","score":0.3846000134944916},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.3183000087738037},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.30570000410079956}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7279000282287598},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7024000287055969},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6934999823570251},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.6134999990463257},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5385000109672546},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4936000108718872},{"id":"https://openalex.org/C60933471","wikidata":"https://www.wikidata.org/wiki/Q17152964","display_name":"Metric dimension","level":5,"score":0.3919999897480011},{"id":"https://openalex.org/C187303228","wikidata":"https://www.wikidata.org/wiki/Q867330","display_name":"Cyclomatic complexity","level":3,"score":0.3846000134944916},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C68103157","wikidata":"https://www.wikidata.org/wiki/Q569347","display_name":"Graph product","level":5,"score":0.3001999855041504},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.28859999775886536},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.28540000319480896},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.27059999108314514},{"id":"https://openalex.org/C67810366","wikidata":"https://www.wikidata.org/wiki/Q835942","display_name":"Interval graph","level":5,"score":0.26919999718666077},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-025-03548-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-025-03548-6","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7160286548","display_name":null,"funder_award_id":"12571376","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7204521761","display_name":null,"funder_award_id":"2022YFA1006400","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G7532292599","display_name":null,"funder_award_id":"2024AIYB003","funder_id":"https://openalex.org/F4320321881","funder_display_name":"Shanghai Municipal Education Commission"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321881","display_name":"Shanghai Municipal Education Commission","ror":"https://ror.org/05tewj457"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W154962059","https://openalex.org/W1489764538","https://openalex.org/W1978707241","https://openalex.org/W2001156667","https://openalex.org/W2025530886","https://openalex.org/W2204805700","https://openalex.org/W2278216163","https://openalex.org/W2493319874","https://openalex.org/W2608213386","https://openalex.org/W2766392964","https://openalex.org/W2809860078","https://openalex.org/W2811294297","https://openalex.org/W2945315293","https://openalex.org/W2996708410","https://openalex.org/W3188648783","https://openalex.org/W3199482904","https://openalex.org/W4221030474","https://openalex.org/W4232896595"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-12-15T00:00:00"}