{"id":"https://openalex.org/W7167908582","doi":"https://doi.org/10.1007/s40314-026-03856-5","title":"Bounds for the Laplacian energy of complex unit gain graphs","display_name":"Bounds for the Laplacian energy of complex unit gain graphs","publication_year":2026,"publication_date":"2026-07-10","ids":{"openalex":"https://openalex.org/W7167908582","doi":"https://doi.org/10.1007/s40314-026-03856-5"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-026-03856-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-026-03856-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","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/A5103225300","display_name":"Jing Zhao","orcid":"https://orcid.org/0000-0002-8528-1045"},"institutions":[{"id":"https://openalex.org/I46482218","display_name":"Anqing Normal University","ror":"https://ror.org/0127ytz78","country_code":"CN","type":"education","lineage":["https://openalex.org/I46482218"]},{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jing Zhao","raw_affiliation_strings":["Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China","Key Laboratory of Intelligent Sensing System and Security (Hubei University), Ministry of Education, Wuhan, China","School of Mathematics and Physics, Anqing Normal University, Anqing, 246133, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China","institution_ids":["https://openalex.org/I75900474"]},{"raw_affiliation_string":"Key Laboratory of Intelligent Sensing System and Security (Hubei University), Ministry of Education, Wuhan, China","institution_ids":["https://openalex.org/I75900474"]},{"raw_affiliation_string":"School of Mathematics and Physics, Anqing Normal University, Anqing, 246133, China","institution_ids":["https://openalex.org/I46482218"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100709941","display_name":"Huiqing Liu","orcid":"https://orcid.org/0000-0001-6703-000X"},"institutions":[{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huiqing Liu","raw_affiliation_strings":["Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China","Key Laboratory of Intelligent Sensing System and Security (Hubei University), Ministry of Education, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China","institution_ids":["https://openalex.org/I75900474"]},{"raw_affiliation_string":"Key Laboratory of Intelligent Sensing System and Security (Hubei University), Ministry of Education, Wuhan, China","institution_ids":["https://openalex.org/I75900474"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103225300"],"corresponding_institution_ids":["https://openalex.org/I46482218","https://openalex.org/I75900474"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.91192426,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"10","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9789999723434448,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9789999723434448,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.0034000000450760126,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.003100000089034438,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6653000116348267},{"id":"https://openalex.org/keywords/unit-circle","display_name":"Unit circle","score":0.510699987411499},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4848000109195709},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4828000068664551},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.47519999742507935},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.43779999017715454},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4025999903678894}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7024000287055969},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6653000116348267},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5343000292778015},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.510699987411499},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4848000109195709},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4828000068664551},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.47519999742507935},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46869999170303345},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.43779999017715454},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.39500001072883606},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.35659998655319214},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.3495999872684479},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3483999967575073},{"id":"https://openalex.org/C78913703","wikidata":"https://www.wikidata.org/wiki/Q5597087","display_name":"Graph energy","level":5,"score":0.2662000060081482},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.25920000672340393}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-026-03856-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-026-03856-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","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":[{"score":0.5433739423751831,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G1978718918","display_name":null,"funder_award_id":"12471325","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6462654507","display_name":null,"funder_award_id":"12371345","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1966432171","https://openalex.org/W2033739210","https://openalex.org/W2063835992","https://openalex.org/W2090143112","https://openalex.org/W2093091655","https://openalex.org/W2123774638","https://openalex.org/W2739914937","https://openalex.org/W3034592402","https://openalex.org/W3111739762","https://openalex.org/W4229706427","https://openalex.org/W4389506675","https://openalex.org/W4392203564"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2026-07-11T00:00:00"}