{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T20:42:29Z","timestamp":1698352949662},"reference-count":10,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5209,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1992,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A Steinhaus graph is a graph with <jats:italic>n<\/jats:italic> vertices whose adjacency matrix (<jats:italic>a<\/jats:italic><jats:sub>i, j<\/jats:sub>) satisfies the condition that <jats:italic>a<\/jats:italic><jats:sub>i, j<\/jats:sub> \uf8fd <jats:italic>a<\/jats:italic><jats:sub>a\u2010\u20101, j\u2010\u20101<\/jats:sub> + <jats:italic>a<\/jats:italic> <jats:sub>i\u2010\u20101, j<\/jats:sub> (mod 2) for each 1 &lt; <jats:italic>i<\/jats:italic> &lt; <jats:italic>j<\/jats:italic> \u2264 <jats:italic>n<\/jats:italic>. It is clear that a Steinhaus graph is determined by its first row. In [3] Bringham and Dutton conjecture that almost all Steinhaus graphs have diameter 2. That is, as <jats:italic>n<\/jats:italic> approaches infinity, the ratio of the number of Steinhaus graphs with <jats:italic>n<\/jats:italic> vertices having diameter 2 to the total number of Steinhaus graphs approaches 1. Here we prove Bringham and Dutton's conjecture.<\/jats:p>","DOI":"10.1002\/jgt.3190160304","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T07:16:41Z","timestamp":1181287001000},"page":"213-219","source":"Crossref","is-referenced-by-count":7,"title":["Almost all steinhaus graphs have diameter 2"],"prefix":"10.1002","volume":"16","author":[{"given":"Neal","family":"Brand","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Probability and Measure","author":"Billingsley P.","year":"1979"},{"key":"e_1_2_1_3_2","unstructured":"R. C.Brigham N.Deo andR. D.Dutton Some properties of Steinhaus graphs. Preprint."},{"key":"e_1_2_1_4_2","unstructured":"R. C.BrighamandR. D.Dutton Distances and diameters in Steinhaus graphs. Preprint."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(81)90217-X"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(81)90217-X"},{"key":"e_1_2_1_7_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_8_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_9_2","first-page":"399","article-title":"Steinhaus graphs","volume":"28","author":"Dymacek W. M.","year":"1979","journal-title":"Numer."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(72)90039-8"},{"key":"e_1_2_1_11_2","volume-title":"One Hundred Problems in Elementary Mathematics","author":"Steinhaus H.","year":"1963"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190160304","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190160304","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T08:21:37Z","timestamp":1698049297000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190160304"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,7]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1992,7]]}},"alternative-id":["10.1002\/jgt.3190160304"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190160304","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,7]]}}}