{"id":"https://openalex.org/W7204528199","doi":"https://doi.org/10.48550/arxiv.2608.27253","title":"Kronecker Products, Polarity Quotients and Large Graph Constructions","display_name":"Kronecker Products, Polarity Quotients and Large Graph Constructions","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204528199","doi":"https://doi.org/10.48550/arxiv.2608.27253"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.27253","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27253","pdf_url":"https://arxiv.org/pdf/2608.27253","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":null,"license_id":null,"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/2608.27253","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066150693","display_name":"Kelly Isham","orcid":"https://orcid.org/0000-0001-7979-0516","observed_orcids":["https://orcid.org/0000-0001-7979-0516"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Isham, Kelly","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027048290","display_name":"Kartik Lakhotia","orcid":"https://orcid.org/0000-0002-9414-8481","observed_orcids":["https://orcid.org/0000-0002-9414-8481","https://orcid.org/0000-0001-7913-5204"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lakhotia, Kartik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006310347","display_name":"Laura Monroe","orcid":"https://orcid.org/0000-0002-7175-0103","observed_orcids":["https://orcid.org/0000-0002-7175-0103"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Monroe, Laura","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066195314","display_name":"Fabrizio Petrini","orcid":"https://orcid.org/0000-0002-4977-7107","observed_orcids":["https://orcid.org/0000-0002-4977-7107"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Petrini, Fabrizio","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/T10849","display_name":"Finite Group Theory Research","score":0.3799000084400177,"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"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.3799000084400177,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.25440001487731934,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.25290000438690186,"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/kronecker-product","display_name":"Kronecker product","score":0.8040000200271606},{"id":"https://openalex.org/keywords/bipartite-graphs","display_name":"bipartite graphs","score":0.949999988079071},{"id":"https://openalex.org/keywords/graph-diameter","display_name":"graph diameter","score":0.7250000238418579},{"id":"https://openalex.org/keywords/moore-bound","display_name":"Moore bound","score":0.9940000176429749},{"id":"https://openalex.org/keywords/generalized-polygons","display_name":"generalized polygons","score":0.5109999775886536},{"id":"https://openalex.org/keywords/degree-diameter-problem","display_name":"degree-diameter problem","score":0.5899999737739563},{"id":"https://openalex.org/keywords/prime-powers","display_name":"prime powers","score":0.5410000085830688}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8184999823570251},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7250000238418579},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.6265000104904175},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6018000245094299},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5529000163078308},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.5370000004768372},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.44690001010894775},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41200000047683716},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38850000500679016},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3440000116825104},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3384000062942505},{"id":"https://openalex.org/C2777361361","wikidata":"https://www.wikidata.org/wiki/Q1112585","display_name":"Polarity (international relations)","level":3,"score":0.3352000117301941},{"id":"https://openalex.org/C159246509","wikidata":"https://www.wikidata.org/wiki/Q5428725","display_name":"Factor graph","level":3,"score":0.32030001282691956},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C68103157","wikidata":"https://www.wikidata.org/wiki/Q569347","display_name":"Graph product","level":5,"score":0.251800000667572},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.27253","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27253","pdf_url":"https://arxiv.org/pdf/2608.27253","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.27253","doi":"https://doi.org/10.48550/arxiv.2608.27253","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.27253","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.27253","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27253","pdf_url":"https://arxiv.org/pdf/2608.27253","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204528199.pdf","grobid_xml":"https://content.openalex.org/works/W7204528199.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W6976624060","https://openalex.org/W7099135102","https://openalex.org/W2023593567","https://openalex.org/W7214091171","https://openalex.org/W2146241813","https://openalex.org/W7172483424","https://openalex.org/W2604831165","https://openalex.org/W1968868239","https://openalex.org/W2039741232","https://openalex.org/W2050866030"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"establish":[4],"a":[5,24,63,73,171],"structural":[6],"compatibility":[7,60],"between":[8],"the":[9,29,52,58,68,109,148],"Kronecker":[10,113,152],"product":[11],"of":[12,31,42,45,76,78,95,99,115,123,125,132,154,162,164,175],"bipartite":[13,59],"graphs":[14,61,77,124,163],"that":[15,49,57,67,100,183],"admit":[16,142],"polarity":[17,20,70,111,117,143,145,156],"and":[18,22,66,102,168,185],"their":[19],"quotients,":[21],"provide":[23],"sharp":[25],"upper":[26],"bound":[27,150],"on":[28],"diameter":[30,81,101,128],"these":[32,36,116,155],"graphs.":[33,112],"We":[34,55],"use":[35],"properties":[37],"to":[38,141],"construct":[39],"new":[40,74,121,160],"families":[41,98,107],"graphs,":[43],"all":[44],"which":[46],"have":[47,62],"orders":[48],"asymptotically":[50],"approach":[51],"Moore":[53,149],"bound.":[54],"show":[56],"natural":[64],"polarity,":[65],"corresponding":[69],"quotients":[71,118,146,157],"comprise":[72],"family":[75,122,161],"any":[79,87,126,179],"even":[80,127],"$2k$":[82],"with":[83,144],"degree":[84,184],"$(q+1)^k$":[85],"for":[86,129,182],"prime":[88,133],"power":[89],"$q$,":[90],"much":[91],"smaller":[92],"than":[93,178],"those":[94],"other":[96],"known":[97,140,181],"field":[103],"order":[104,176],"$q$.":[105],"These":[106],"generalize":[108],"Erd\u0151s-R\u00e9nyi-Brown":[110],"products":[114,153],"give":[119,158],"another":[120,159],"every":[130],"pair":[131],"powers":[134],"$q,r$.":[135],"Certain":[136],"generalized":[137],"polygons":[138],"are":[139],"approaching":[147],"asymptotically.":[151],"diameters":[165],"$2$,":[166],"$3$":[167],"$5$,":[169],"including":[170],"diameter-$3$":[172],"degree-$18$":[173],"graph":[174],"larger":[177],"previously":[180],"diameter.":[186]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-29T00:00:00"}