{"id":"https://openalex.org/W7223910062","doi":"https://doi.org/10.47443/dml.2026.248","title":"Irregularity and Near Star Graphs","display_name":"Irregularity and Near Star Graphs","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7223910062","doi":"https://doi.org/10.47443/dml.2026.248"},"language":"en","primary_location":{"id":"doi:10.47443/dml.2026.248","doi":"https://doi.org/10.47443/dml.2026.248","is_oa":true,"landing_page_url":"https://doi.org/10.47443/dml.2026.248","pdf_url":"https://doi.org/10.47443/dml.2026.248","source":{"id":"https://openalex.org/S4210212609","display_name":"Discrete Mathematics Letters","issn_l":"2664-2557","issn":["2664-2557"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","norway-1","poland-20","russia-white-list-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics Letters","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.47443/dml.2026.248","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030332288","display_name":"Allan Bickle","orcid":"https://orcid.org/0000-0002-7739-607X","observed_orcids":["https://orcid.org/0000-0002-7739-607X"]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Allan Bickle","raw_affiliation_strings":["Department of Mathematics , Purdue University , West Lafayette , IN 47907 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Purdue University , West Lafayette , IN 47907 , USA","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030332288"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.86934422,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":null,"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":0.9990000128746033,"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":0.9990000128746033,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.0006000000284984708,"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/T12292","display_name":"Graph Theory and Algorithms","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/first-zagreb-index","display_name":"first Zagreb index","score":0.9900000095367432},{"id":"https://openalex.org/keywords/extremal-graphs","display_name":"extremal graphs","score":0.9520000219345093},{"id":"https://openalex.org/keywords/degree-sequences","display_name":"degree sequences","score":0.4959999918937683}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.715399980545044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6686000227928162},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5881999731063843},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5094000101089478},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.4724999964237213},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.4327000081539154},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.353300005197525},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.2757999897003174},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.24240000545978546}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.47443/dml.2026.248","doi":"https://doi.org/10.47443/dml.2026.248","is_oa":true,"landing_page_url":"https://doi.org/10.47443/dml.2026.248","pdf_url":"https://doi.org/10.47443/dml.2026.248","source":{"id":"https://openalex.org/S4210212609","display_name":"Discrete Mathematics Letters","issn_l":"2664-2557","issn":["2664-2557"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","norway-1","poland-20","russia-white-list-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics Letters","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:56fd0538be774f9fa4f5e6bcb73bfe17","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/56fd0538be774f9fa4f5e6bcb73bfe17","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,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete Mathematics Letters, Vol 18, Pp 137-141 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.47443/dml.2026.248","doi":"https://doi.org/10.47443/dml.2026.248","is_oa":true,"landing_page_url":"https://doi.org/10.47443/dml.2026.248","pdf_url":"https://doi.org/10.47443/dml.2026.248","source":{"id":"https://openalex.org/S4210212609","display_name":"Discrete Mathematics Letters","issn_l":"2664-2557","issn":["2664-2557"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","norway-1","poland-20","russia-white-list-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics Letters","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223910062.pdf","grobid_xml":"https://content.openalex.org/works/W7223910062.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3022643563","https://openalex.org/W2155802616","https://openalex.org/W4291782745","https://openalex.org/W2085393097","https://openalex.org/W7217532575","https://openalex.org/W2104917052","https://openalex.org/W4388304256","https://openalex.org/W105367266","https://openalex.org/W2950373754","https://openalex.org/W4224220633"],"abstract_inverted_index":{"where":[0],"the":[1,18,38,55],"sum":[2],"is":[3,30],"over":[4],"all":[5,33],"edges":[6,28],"of":[7,20,46,52],"G.In":[8],"2005,":[9],"Hansen":[10],"and":[11,26,36,49,77],"M\u00e9lot":[12],"proved":[13],"an":[14],"upper":[15],"bound":[16],"on":[17,23,74],"irregularity":[19,76],"a":[21,42],"graph":[22],"n":[24],"vertices":[25],"m":[27],"that":[29,64],"attained":[31],"for":[32,71],"feasible":[34],"values,":[35],"characterized":[37],"extremal":[39,56,69],"graphs.We":[40],"give":[41],"much":[43],"shorter":[44],"proof":[45],"this":[47],"result,":[48],"discuss":[50],"some":[51],"its":[53],"implications.Denoting":[54],"graphs":[57,70],"as":[58,68],"near":[59],"k-star":[60],"graphs,":[61],"we":[62],"show":[63],"they":[65],"sometimes":[66],"occur":[67],"related":[72],"problems":[73],"sigma":[75],"first":[78],"Zagreb":[79],"index.":[80]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-28T00:00:00"}