{"id":"https://openalex.org/W7204786595","doi":"https://doi.org/10.48550/arxiv.2608.27624","title":"Uniformly Weighted Graphical Designs","display_name":"Uniformly Weighted Graphical Designs","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204786595","doi":"https://doi.org/10.48550/arxiv.2608.27624"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.27624","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27624","pdf_url":"https://arxiv.org/pdf/2608.27624","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/2608.27624","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089714379","display_name":"Zawad Chowdhury","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chowdhury, Zawad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5047323505","display_name":"Rekha R. Thomas","orcid":"https://orcid.org/0000-0003-2189-2303","observed_orcids":["https://orcid.org/0000-0003-2189-2303"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas, Rekha R.","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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.5131999850273132,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.5131999850273132,"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/T10849","display_name":"Finite Group Theory Research","score":0.14069999754428864,"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/T11130","display_name":"Coding theory and cryptography","score":0.10360000282526016,"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/graph-design","display_name":"graph design","score":0.5},{"id":"https://openalex.org/keywords/threshold-graphs","display_name":"threshold graphs","score":0.9160000085830688},{"id":"https://openalex.org/keywords/orthogonal-arrays","display_name":"orthogonal arrays","score":0.8730000257492065},{"id":"https://openalex.org/keywords/linear-codes","display_name":"linear codes","score":0.7210000157356262},{"id":"https://openalex.org/keywords/irreducible-polynomials","display_name":"irreducible polynomials","score":0.6990000009536743},{"id":"https://openalex.org/keywords/polyhedral-characterization","display_name":"polyhedral characterization","score":0.5759999752044678}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7817999720573425},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5982000231742859},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5950999855995178},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5199999809265137},{"id":"https://openalex.org/C122451846","wikidata":"https://www.wikidata.org/wiki/Q5150824","display_name":"Combinatorial design","level":2,"score":0.4659000039100647},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.46070000529289246},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4424999952316284},{"id":"https://openalex.org/C689293","wikidata":"https://www.wikidata.org/wiki/Q751484","display_name":"Block design","level":2,"score":0.3684999942779541},{"id":"https://openalex.org/C73361133","wikidata":"https://www.wikidata.org/wiki/Q4810150","display_name":"Association scheme","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.3257000148296356},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C2983050975","wikidata":"https://www.wikidata.org/wiki/Q88287214","display_name":"Block structure","level":3,"score":0.272599995136261},{"id":"https://openalex.org/C133875400","wikidata":"https://www.wikidata.org/wiki/Q692823","display_name":"Strongly regular graph","level":5,"score":0.25679999589920044},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.27624","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27624","pdf_url":"https://arxiv.org/pdf/2608.27624","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.2608.27624","doi":"https://doi.org/10.48550/arxiv.2608.27624","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.27624","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:2608.27624","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27624","pdf_url":"https://arxiv.org/pdf/2608.27624","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/W7204786595.pdf","grobid_xml":"https://content.openalex.org/works/W7204786595.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1571018443","https://openalex.org/W4415310647","https://openalex.org/W7160401836"],"related_works":["https://openalex.org/W4286762041","https://openalex.org/W4415310647","https://openalex.org/W4392461305","https://openalex.org/W4417530933","https://openalex.org/W2520549594","https://openalex.org/W2086892065","https://openalex.org/W3040906459","https://openalex.org/W2614176506","https://openalex.org/W2962988436","https://openalex.org/W4313408524"],"abstract_inverted_index":{"A":[0,30],"graphical":[1,59,88],"design":[2,31],"is":[3,32],"a":[4,9,13,111,139,155],"subset":[5],"of":[6,8,25,85,98,114,123,134,142,145],"vertices":[7],"graph,":[10],"along":[11],"with":[12],"weight":[14],"for":[15,158],"each":[16],"chosen":[17,23],"vertex,":[18],"that":[19,100,117],"can":[20],"perfectly":[21],"average":[22],"subspaces":[24],"functions":[26],"on":[27],"the":[28,37,83,115,119,143],"graph.":[29],"uniformly":[33,57,67,86,131,171],"weighted":[34,58,68,87,132,172],"if":[35],"all":[36,130],"weights":[38],"are":[39,56,164],"equal,":[40],"and":[41,53,90,102,121,137,148],"several":[42,96],"well-known":[43],"combinatorial":[44,50],"objects":[45],"such":[46,106],"as":[47],"orthogonal":[48,150],"arrays,":[49],"block":[51],"designs":[52,69,133],"t-wise":[54],"permutations":[55],"designs.":[60,107,125,173],"While":[61],"one":[62],"might":[63],"expect":[64],"to":[65,94,167],"see":[66],"in":[70],"structured":[71],"graphs,":[72,136],"they":[73],"do":[74,103],"not":[75,104],"always":[76],"exist.":[77],"In":[78,126],"this":[79],"paper":[80],"we":[81,128],"characterize":[82,129],"existence":[84,120],"designs,":[89],"use":[91],"our":[92],"result":[93],"provide":[95,138,154],"families":[97,169],"graphs":[99,159],"have,":[101,105],"Our":[108],"results":[109],"offer":[110],"polyhedral":[112],"view":[113],"structures":[116],"control":[118],"cardinalities":[122],"these":[124],"particular,":[127],"threshold":[135],"geometric":[140],"proof":[141],"duality":[144],"linear":[146,149],"codes":[147],"arrays.":[151],"We":[152],"also":[153],"novel":[156],"construction":[157],"whose":[160],"Laplacian":[161],"characteristic":[162],"polynomials":[163],"almost":[165],"irreducible,":[166],"produce":[168],"without":[170]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-01T00:00:00"}