{"id":"https://openalex.org/W2141011466","doi":"https://doi.org/10.1002/jgt.3190200105","title":"Generalized steinhaus graphs","display_name":"Generalized steinhaus graphs","publication_year":1995,"publication_date":"1995-08-01","ids":{"openalex":"https://openalex.org/W2141011466","doi":"https://doi.org/10.1002/jgt.3190200105","mag":"2141011466"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190200105","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190200105","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"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002299079","display_name":"Margaret Morton","orcid":null},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Margaret Morton","raw_affiliation_strings":["Department of Mathematics University of Auckland Auckland, New Zealand","Department of Mathematics, University of Auckland, Auckland, New Zealand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Auckland Auckland, New Zealand","institution_ids":["https://openalex.org/I154130895"]},{"raw_affiliation_string":"Department of Mathematics, University of Auckland, Auckland, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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":0.738,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.67910448,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"1","first_page":"47","last_page":"58"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998999834060669,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998999834060669,"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":0.9976999759674072,"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/T11476","display_name":"Graph theory and applications","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8127200603485107},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7924844622612},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5638510584831238},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4902039170265198},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.42918941378593445},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41639846563339233}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8127200603485107},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7924844622612},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5638510584831238},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4902039170265198},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.42918941378593445},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41639846563339233},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190200105","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190200105","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1970557422","https://openalex.org/W1998400388","https://openalex.org/W2035687898","https://openalex.org/W2076880497","https://openalex.org/W2085536555","https://openalex.org/W2093304883","https://openalex.org/W2131815672","https://openalex.org/W2901284226","https://openalex.org/W4235934183","https://openalex.org/W4298443330","https://openalex.org/W6600971645"],"related_works":["https://openalex.org/W178365807","https://openalex.org/W2081441417","https://openalex.org/W4240676090","https://openalex.org/W1970375080","https://openalex.org/W4386544785","https://openalex.org/W16157476","https://openalex.org/W1555836633","https://openalex.org/W1522717445","https://openalex.org/W2116374711","https://openalex.org/W2980963558"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"generalized":[2,146,158,203],"Steinhaus":[3,83,147,159,204],"graph":[4,13,133],"of":[5,70,104,111,122,156,166,171],"order":[6],"n":[7,15,34,46],"and":[8,63,75,100,108,183,209],"type":[9],"s":[10,38,58,71],"is":[11,161],"a":[12,21,120],"with":[14,163],"vertices":[16],"whose":[17],"adjacency":[18],"matrix":[19],"(":[20,39,59,72],"i,j":[22],")":[23,61,74],"satisfies":[24],"the":[25,153,164],"relation":[26],"magnified":[27],"image":[28],"where":[29],"2":[30,208],"\u2266":[31,33,43,45,55,57],"i":[32,36,40,60,73],"\u22121,":[35],"+":[37],"\u2212":[41],"1":[42],"j":[44],",":[47,114,190],"c":[48,64,76],"r,i,j":[49,77],"\u03f5":[50],"{0,1}":[51],"for":[52],"all":[53,145,202,211],"0":[54],"r":[56],"\u22121":[62],"s(i)\u22121,i,j":[65],"=":[66],"1.":[67],"The":[68],"values":[69],"are":[78,92,125,173],"fixed":[79],"but":[80],"arbitrary.":[81],"Generalized":[82],"graphs":[84,148,160,172,205],"in":[85,132],"which":[86,128],"each":[87],"edge":[88],"has":[89],"probability":[90],"\u00bd":[91],"considered.":[93],"In":[94],"an":[95],"article":[96],"by":[97,175,198],"A.":[98],"Blass":[99],"F.":[101,176],"Harary":[102],"[\u201cProperties":[103],"Almost":[105],"All":[106],"Graphs":[107],"Complexes,\u201d":[109],"Journal":[110],"Graph":[112],"Theory":[113],"Vol.":[115,191],"3":[116],"(1976),":[117],"pp.":[118,194],"225\u2013240],":[119],"collection":[121],"first\u2010order":[123,130,154],"axioms":[124],"given":[126],"from":[127],"any":[129],"property":[131],"theory":[134,155,165],"or":[135],"its":[136],"negation":[137],"can":[138],"be":[139],"deduced.":[140],"We":[141,196],"show":[142],"that":[143,200],"almost":[144,201],"satisfy":[149],"these":[150],"axioms.":[151],"Thus":[152],"random":[157,167],"identical":[162],"graphs.":[168],"Quasi\u2010random":[169],"properties":[170],"described":[174],"R.":[177,180,184],"K.":[178],"Chung,":[179],"L.":[181],"Graham,":[182],"M.":[185],"Wilson,":[186],"[\u201cQuasi\u2010Random":[187],"Graphs,\u201d":[188],"Combinatorica":[189],"9":[192],"(1989),":[193],"345\u2013362].":[195],"conclude":[197],"demonstrating":[199],"obey":[206],"Property":[207],"hence":[210],"equivalent":[212],"quasi\u2010random":[213],"properties.":[214],"\u00a9":[215],"1996":[216],"John":[217],"Wiley":[218],"&amp;":[219],"Sons,":[220],"Inc.":[221]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
