{"id":"https://openalex.org/W7134837599","doi":"https://doi.org/10.48550/arxiv.2603.08354","title":"On the Dual Drazin Inverse of Adjacency Matrices of Dual-number-Weighted Digraphs","display_name":"On the Dual Drazin Inverse of Adjacency Matrices of Dual-number-Weighted Digraphs","publication_year":2026,"publication_date":"2026-03-09","ids":{"openalex":"https://openalex.org/W7134837599","doi":"https://doi.org/10.48550/arxiv.2603.08354"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2603.08354","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128662204","display_name":"Yue Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Yue","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028792370","display_name":"Daochang Zhang","orcid":"https://orcid.org/0000-0002-9648-362X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Daochang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128638119","display_name":"Zhongshan Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Zhongshan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5051060964","display_name":"Frank J. Hall","orcid":"https://orcid.org/0000-0002-3061-3671"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hall, Frank J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.8144000172615051,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.8144000172615051,"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":0.06340000033378601,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.020899999886751175,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/drazin-inverse","display_name":"Drazin inverse","score":0.7484999895095825},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.6628999710083008},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6498000025749207},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.6319000124931335},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5349000096321106},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.516700029373169},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5149999856948853},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4228000044822693}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8109999895095825},{"id":"https://openalex.org/C2777795832","wikidata":"https://www.wikidata.org/wiki/Q4521948","display_name":"Drazin inverse","level":3,"score":0.7484999895095825},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6628999710083008},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6498000025749207},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.6319000124931335},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5882999897003174},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5349000096321106},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.516700029373169},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5149999856948853},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4228000044822693},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.3889000117778778},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.3824000060558319},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.36390000581741333},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36340001225471497},{"id":"https://openalex.org/C76134657","wikidata":"https://www.wikidata.org/wiki/Q370634","display_name":"Generalized inverse","level":3,"score":0.3546000123023987},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31439998745918274},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.29440000653266907},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.2694000005722046}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2603.08354","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2603.08354","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08354","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2603.08354","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"motivation":[1],"of":[2,12,19,35,122],"this":[3],"paper":[4],"is":[5,78,98],"to":[6,50,100],"investigate":[7],"the":[8,24,31,60,75,86,101,114],"dual":[9,25,32,36,102,115,119],"Drazin":[10,33,103,120],"inverse":[11,34,88,104,117,121],"adjacency":[13,96,124],"matrices":[14,40,97],"arising":[15],"from":[16],"several":[17],"classes":[18],"connected":[20],"dual-number-weighted":[21],"digraphs":[22],"over":[23],"complex":[26,37],"algebra.":[27],"Explicit":[28],"formulas":[29,112],"for":[30,66,74,82,92,105,113,126],"anti-triangular":[38],"block":[39,94],"are":[41,48,64],"derived":[42],"under":[43],"suitable":[44],"assumptions.":[45],"These":[46],"results":[47],"applied":[49],"DN-DS":[51,67],"digraphs,":[52,54,68],"DN-DLS":[53,83],"and":[55,80,118],"DN-DW":[56,106,127],"digraphs.":[57,84,107,128],"In":[58],"particular,":[59],"assumptions":[61],"in":[62,72,90],"\\cite{AMPMJM2026}":[63,73],"weakened":[65],"an":[69],"open":[70],"problem":[71],"case":[76],"$BC=0$":[77],"generalized":[79],"solved":[81],"And":[85],"group":[87,116],"result":[89],"\\cite{MNSEJAA2022}":[91],"bipartite":[93],"form":[95],"extended":[99],"We":[108],"further":[109],"derive":[110],"explicit":[111],"another":[123],"matrix":[125]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-03-11T00:00:00"}
