{"id":"https://openalex.org/W4386907425","doi":"https://doi.org/10.48550/arxiv.2309.10317","title":"Projective dimension and regularity of edge ideals of some vertex-weighted oriented unicyclic graphs","display_name":"Projective dimension and regularity of edge ideals of some vertex-weighted oriented unicyclic graphs","publication_year":2023,"publication_date":"2023-09-19","ids":{"openalex":"https://openalex.org/W4386907425","doi":"https://doi.org/10.48550/arxiv.2309.10317"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2309.10317","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.10317","pdf_url":"https://arxiv.org/pdf/2309.10317","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2309.10317","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004737260","display_name":"Guangjun Zhu","orcid":"https://orcid.org/0000-0002-7196-1090","observed_orcids":["https://orcid.org/0000-0002-7196-1090"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Guangjun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5115593867","display_name":"Hong Wang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Hong","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":true,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9970999956130981,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9970999956130981,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.0003000000142492354,"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/T11476","display_name":"Graph theory and applications","score":9.999999747378752e-05,"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/projective-dimension","display_name":"projective dimension","score":0.8880000114440918},{"id":"https://openalex.org/keywords/castelnuovo-mumford-regularity","display_name":"Castelnuovo-Mumford regularity","score":0.9929999709129333},{"id":"https://openalex.org/keywords/edge-ideals","display_name":"edge ideals","score":1.0},{"id":"https://openalex.org/keywords/vertex-weighted-graphs","display_name":"vertex-weighted graphs","score":0.7720000147819519},{"id":"https://openalex.org/keywords/monomial-ideals","display_name":"monomial ideals","score":0.7350000143051147}],"concepts":[{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7594403028488159},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7326642870903015},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6828315258026123},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.5803831815719604},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5065959692001343},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4888381361961365},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45614007115364075},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3940884470939636},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1701790988445282},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1680455505847931},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06504437327384949}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2309.10317","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.10317","pdf_url":"https://arxiv.org/pdf/2309.10317","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2309.10317","doi":"https://doi.org/10.48550/arxiv.2309.10317","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2309.10317","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2309.10317","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2309.10317","pdf_url":"https://arxiv.org/pdf/2309.10317","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4611607877","display_name":null,"funder_award_id":"BK20221353","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"}],"funders":[{"id":"https://openalex.org/F4320321605","display_name":"Government of Jiangsu Province","ror":"https://ror.org/004svx814"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386907425.pdf","grobid_xml":"https://content.openalex.org/works/W4386907425.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2762043281","https://openalex.org/W2795763531"],"related_works":["https://openalex.org/W3160630156","https://openalex.org/W2937618907","https://openalex.org/W2970445512","https://openalex.org/W2788629047","https://openalex.org/W3130736747","https://openalex.org/W2926251309","https://openalex.org/W3201741970","https://openalex.org/W2980749853","https://openalex.org/W3118549010","https://openalex.org/W2801779191"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"provide":[4],"some":[5,41],"exact":[6],"formulas":[7,24,47],"for":[8,59],"the":[9,13,29,32,34,54],"projective":[10],"dimension":[11],"and":[12,53],"regularity":[14],"of":[15,18,28,31,36],"edge":[16],"ideals":[17],"vertex-weighted":[19],"oriented":[20],"unicyclic":[21],"graphs.":[22],"These":[23],"are":[25,48],"in":[26],"function":[27],"weight":[30],"vertices,":[33],"numbers":[35],"edges.":[37],"We":[38],"also":[39],"give":[40],"examples":[42],"to":[43,50],"show":[44],"that":[45,56],"these":[46],"related":[49],"direction":[51],"selection":[52],"assumptions":[55],"$w(x)\\geq":[57],"2$":[58],"any":[60],"vertex":[61],"$x$":[62],"cannot":[63],"be":[64],"dropped.":[65]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2023-09-21T00:00:00"}