{"id":"https://openalex.org/W2131815672","doi":"https://doi.org/10.1002/jgt.3190160304","title":"Almost all steinhaus graphs have diameter 2","display_name":"Almost all steinhaus graphs have diameter 2","publication_year":1992,"publication_date":"1992-07-01","ids":{"openalex":"https://openalex.org/W2131815672","doi":"https://doi.org/10.1002/jgt.3190160304","mag":"2131815672"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190160304","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190160304","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111934880","display_name":"Neal Brand","orcid":null},"institutions":[{"id":"https://openalex.org/I123534392","display_name":"University of North Texas","ror":"https://ror.org/00v97ad02","country_code":"US","type":"education","lineage":["https://openalex.org/I123534392"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Neal Brand","raw_affiliation_strings":["Department of Mathematics University of North Texas Denton Texas","Department of Mathematics, University of North Texas, Denton, Texas"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of North Texas Denton Texas","institution_ids":["https://openalex.org/I123534392"]},{"raw_affiliation_string":"Department of Mathematics, University of North Texas, Denton, Texas","institution_ids":["https://openalex.org/I123534392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111934880"],"corresponding_institution_ids":["https://openalex.org/I123534392"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":2.1564,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.89152741,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"3","first_page":"213","last_page":"219"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9957000017166138,"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"}},"topics":[{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9957000017166138,"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"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9760000109672546,"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":0.9753999710083008,"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/combinatorics","display_name":"Combinatorics","score":0.8664122819900513},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.793684720993042},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.657012939453125},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.4987454414367676},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4969382584095001},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3971739113330841}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8664122819900513},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.793684720993042},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.657012939453125},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.4987454414367676},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4969382584095001},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3971739113330841}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190160304","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190160304","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1608430771","https://openalex.org/W2070298414","https://openalex.org/W2072280917","https://openalex.org/W4300577719"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W4297950433","https://openalex.org/W1973978937","https://openalex.org/W4287023968","https://openalex.org/W4288279572","https://openalex.org/W4286909116","https://openalex.org/W4292635168"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"Steinhaus":[2,50,67,84,97],"graph":[3,6,51],"is":[4,46,52],"a":[5,14,22,26,30,49],"with":[7,86],"n":[8,43,75,87],"vertices":[9,88],"whose":[10],"adjacency":[11],"matrix":[12],"(":[13],"i,":[15,23],"j":[16,24,32,41],")":[17],"satisfies":[18],"the":[19,78,81,93],"condition":[20],"that":[21,48,64],"\uf8fd":[25],"a\u2010\u20101,":[27],"j\u2010\u20101":[28],"+":[29],"i\u2010\u20101,":[31],"(mod":[33],"2)":[34],"for":[35],"each":[36],"1":[37],"&lt;":[38,40],"i":[39],"\u2264":[42],".":[44],"It":[45],"clear":[47],"determined":[53],"by":[54],"its":[55],"first":[56],"row.":[57],"In":[58],"[3]":[59],"Bringham":[60,104],"and":[61,105],"Dutton":[62],"conjecture":[63],"almost":[65],"all":[66],"graphs":[68,85,98],"have":[69],"diameter":[70,90],"2.":[71],"That":[72],"is,":[73],"as":[74],"approaches":[76,99],"infinity,":[77],"ratio":[79],"of":[80,83,96],"number":[82,95],"having":[89],"2":[91],"to":[92],"total":[94],"1.":[100],"Here":[101],"we":[102],"prove":[103],"Dutton's":[106],"conjecture.":[107]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
