{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T05:40:19Z","timestamp":1698385219998},"reference-count":17,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4084,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1995,8]]},"abstract":"Abstract<\/jats:title>A generalized Steinhaus graph of order n<\/jats:italic> and type s<\/jats:italic> is a graph with n<\/jats:italic> vertices whose adjacency matrix (a<\/jats:italic>i,j<\/jats:sub>) satisfies the relation magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap> where 2 \u2266i<\/jats:italic>\u2266n<\/jats:italic>\u22121, i<\/jats:italic> + s<\/jats:italic>(i<\/jats:italic> \u2212 1 \u2266 j<\/jats:italic> \u2266 n<\/jats:italic>, c<\/jats:italic>r,i,j<\/jats:sub> \u03f5 {0,1} for all 0 \u2266 r<\/jats:italic> \u2266 s<\/jats:italic>(i<\/jats:italic>) \u22121 and c<\/jats:italic>s(i)\u22121,i,j<\/jats:sub> = 1. The values of s<\/jats:italic>(i<\/jats:italic>) and c<\/jats:italic>r,i,j<\/jats:sub> are fixed but arbitrary. Generalized Steinhaus graphs in which each edge has probability \u00bd are considered. In an article by A. Blass and F. Harary [\u201cProperties of Almost All Graphs and Complexes,\u201d Journal of Graph Theory<\/jats:italic>, Vol. 3 (1976), pp. 225\u2013240], a collection of first\u2010order axioms are given from which any first\u2010order property in graph theory or its negation can be deduced. We show that almost all generalized Steinhaus graphs satisfy these axioms. Thus the first\u2010order theory of random generalized Steinhaus graphs is identical with the theory of random graphs. Quasi\u2010random properties of graphs are described by F. R. K. Chung, R. L. Graham, and R. M. Wilson, [\u201cQuasi\u2010Random Graphs,\u201d Combinatorica<\/jats:italic>, Vol. 9 (1989), pp. 345\u2013362]. We conclude by demonstrating that almost all generalized Steinhaus graphs obey Property 2 and hence all equivalent quasi\u2010random properties. \u00a9 1996 John Wiley & Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190200105","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T15:24:27Z","timestamp":1181229867000},"page":"47-58","source":"Crossref","is-referenced-by-count":0,"title":["Generalized steinhaus graphs"],"prefix":"10.1002","volume":"20","author":[{"given":"Neal","family":"Brand","sequence":"first","affiliation":[]},{"given":"Margaret","family":"Morton","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(88)90189-6"},{"key":"e_1_2_1_3_2","first-page":"45","article-title":"Regular Steinhaus graphs","volume":"66","author":"Bailey C. K.","year":"1988","journal-title":"Congres. Numer."},{"key":"e_1_2_1_4_2","volume-title":"Probability and Measure","author":"Billingsley P.","year":"1979"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190030305"},{"key":"e_1_2_1_6_2","volume-title":"Random Graphs","author":"Bollob\u00e1s B.","year":"1985"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190160304"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(93)90036-N"},{"key":"e_1_2_1_9_2","unstructured":"N.BrandandS.Jackson Propeties of classes of random graphs. Preprint."},{"key":"e_1_2_1_10_2","unstructured":"R. C.Bingham N.Deo andR. D.Dutton Some properties of Steinhaus graphs. Preprint."},{"key":"e_1_2_1_11_2","first-page":"7","article-title":"Distances and diameters in Steinhaus graphs","volume":"76","author":"Brigham R. C.","year":"1990","journal-title":"Congres. Number."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02125347"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(86)90064-6"},{"key":"e_1_2_1_14_2","first-page":"41","article-title":"Small cycles in Steinhaus graphs","volume":"70","author":"Dymacek W. M.","year":"1990","journal-title":"Congres. Numer."},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.2307\/2272945"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(88)90040-8"},{"key":"e_1_2_1_17_2","series-title":"LMS Lecture Notes Series","first-page":"173","volume-title":"Surveys in Combinatorics 1987","author":"Thomason A.","year":"1987"},{"key":"e_1_2_1_18_2","first-page":"307","article-title":"Pseudo\u2010random graphs","volume":"33","author":"Thomason A.","year":"1987","journal-title":"Ann. of Discrete Math."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190200105","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190200105","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T20:18:58Z","timestamp":1698351538000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190200105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,8]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1995,8]]}},"alternative-id":["10.1002\/jgt.3190200105"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190200105","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,8]]}}}