{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T08:36:16Z","timestamp":1776760576616,"version":"3.51.2"},"reference-count":31,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[1987,1,1]],"date-time":"1987-01-01T00:00:00Z","timestamp":536457600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,9,10]],"date-time":"2013-09-10T00:00:00Z","timestamp":1378771200000},"content-version":"vor","delay-in-days":9749,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["European Journal of Combinatorics"],"published-print":{"date-parts":[[1987,1]]},"DOI":"10.1016\/s0195-6698(87)80023-9","type":"journal-article","created":{"date-parts":[[2013,9,10]],"date-time":"2013-09-10T08:55:59Z","timestamp":1378803359000},"page":"73-102","source":"Crossref","is-referenced-by-count":17,"title":["Root Systems and The Johnson and Hamming Graphs"],"prefix":"10.1016","volume":"8","author":[{"given":"Paul","family":"Terwilliger","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0195-6698(87)80023-9_bib1","doi-asserted-by":"crossref","first-page":"219","DOI":"10.2140\/pjm.1968.25.219","article-title":"On the tetrahedral graph","volume":"25","author":"Aigner","year":"1968","journal-title":"Pacific J. Math."},{"key":"10.1016\/S0195-6698(87)80023-9_bib2","series-title":"Algebraic Combinatorics I: Association Schemes, Benjamin-Cummings Lecture Note Series","author":"Bennai","year":"1984"},{"key":"10.1016\/S0195-6698(87)80023-9_bib3","series-title":"Algebraic Graph Theory","author":"Biggs","year":"1974"},{"key":"10.1016\/S0195-6698(87)80023-9_bib4","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/BF00148146","article-title":"Automorphic graphs and the Krein condition","volume":"5","author":"Biggs","year":"1976","journal-title":"Geom. Dedicata"},{"key":"10.1016\/S0195-6698(87)80023-9_bib5","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1016\/S0021-9800(67)80104-2","article-title":"A characterization of tetrahedral graphs","volume":"3","author":"Bose","year":"1967","journal-title":"J. Combin. Theory"},{"key":"10.1016\/S0195-6698(87)80023-9_bib6","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/BF02579277","article-title":"There are only finitely many distance-transitive graphs of given valency greater than two","volume":"2","author":"Cameron","year":"1982","journal-title":"Combinatorica"},{"key":"10.1016\/S0195-6698(87)80023-9_bib7","first-page":"305","article-title":"Line graphs","volume":"43","author":"Cameron","year":"1976","journal-title":"root systems, and elliptic geometry, J. Algebra"},{"key":"10.1016\/S0195-6698(87)80023-9_bib8","first-page":"604","article-title":"The uniqueness and non-uniqueness of the triangular association schemes","volume":"3","author":"Chang","year":"1959","journal-title":"Sci. Record, Math. New Ser."},{"key":"10.1016\/S0195-6698(87)80023-9_bib9","article-title":"A synopsis of known distance-regular graphs with large diameters","volume":"168\/81","author":"Cohen","year":"1981","journal-title":"Mathematisch Centrum ZW"},{"key":"10.1016\/S0195-6698(87)80023-9_bib10","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1214\/aoms\/1177706724","article-title":"The uniqueness of the triangular association scheme","volume":"29","author":"Connor","year":"1958","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0195-6698(87)80023-9_bib11","article-title":"An algebraic approach to the association schemes of coding theory","volume":"Suppl. 10","author":"Delsarte","year":"1973","journal-title":"Phillips Res. Rep."},{"key":"10.1016\/S0195-6698(87)80023-9_bib12","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/S0021-9800(69)80085-2","article-title":"A characterization of the T.-graph","volume":"6","author":"Dowling","year":"1969","journal-title":"J. Combin. Theory"},{"key":"10.1016\/S0195-6698(87)80023-9_bib13","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/0097-3165(81)90007-8","article-title":"Characterization of H(n","volume":"31","author":"Egawa","year":"1981","journal-title":"q) by the parameters, J. Combin. Theory, Ser. A"},{"key":"10.1016\/S0195-6698(87)80023-9_bib14","series-title":"Research Notes in Mathematics","article-title":"Geometry of Coxeter Groups","author":"Hiller","year":"1982"},{"key":"10.1016\/S0195-6698(87)80023-9_bib15","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1214\/aoms\/1177705914","article-title":"On the uniqueness of the triangular association scheme","volume":"31","author":"Hoffman","year":"1960","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0195-6698(87)80023-9_bib16","series-title":"Introduction to Lie Algebras and Representation Theory","author":"Humphreys","year":"1976"},{"key":"10.1016\/S0195-6698(87)80023-9_bib17","first-page":"789","article-title":"A diameter bound for distance-regular graphs","volume":"271","author":"Ivanov","year":"1983","journal-title":"Soviet Math. Dokl."},{"key":"10.1016\/S0195-6698(87)80023-9_bib18","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/0095-8956(77)90070-3","article-title":"On the uniqueness of the tetrahedral association schemes","volume":"22","author":"Liebler","year":"1977","journal-title":"J. Combin. Theory, Ser. B"},{"key":"10.1016\/S0195-6698(87)80023-9_bib19","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/BF02579282","article-title":"Infinite distance-transitive graphs of finite valency","volume":"2","author":"McPherson","year":"1982","journal-title":"Combinatorica"},{"key":"10.1016\/S0195-6698(87)80023-9_bib20","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/0012-365X(82)90057-7","article-title":"Characterization of the odd graphs Ok by parameters","volume":"42","author":"Moon","year":"1982","journal-title":"Discrete Math."},{"key":"10.1016\/S0195-6698(87)80023-9_bib21","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0095-8956(82)90040-5","article-title":"Characterization of the graphs of the Johnson schemes","volume":"33","author":"Moon","year":"1982","journal-title":"G(3k, k) and G(3k + 1, k), J. Combin. Theory, Ser. B"},{"key":"10.1016\/S0195-6698(87)80023-9_bib22","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/0095-8956(82)90045-4","article-title":"On the uniqueness of the graphs G(n, k) of the Johnson schemes","volume":"Ser. B 33","author":"Moon","year":"1982","journal-title":"J. Combin. Theory"},{"key":"10.1016\/S0195-6698(87)80023-9_bib23","series-title":"On the uniqueness of the tetrahedral association scheme, Ph.D. Thesis","author":"Rolland","year":"1976"},{"key":"10.1016\/S0195-6698(87)80023-9_bib24","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1214\/aoms\/1177706357","article-title":"On a Characterization of the triangular association scheme","volume":"30","author":"Shrikhande","year":"1959","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0195-6698(87)80023-9_bib25","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1214\/aoms\/1177706207","article-title":"The uniqueness of the LZ association scheme","volume":"30","author":"Shrikhande","year":"1959","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/S0195-6698(87)80023-9_bib26","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/0095-8956(82)90034-X","article-title":"The diameter of bipartite distance-regular graphs","volume":"32","author":"Terwilliger","year":"1982","journal-title":"J. Combin. Theory, Ser. B"},{"key":"10.1016\/S0195-6698(87)80023-9_bib27","unstructured":"P. Terwilliger: Distance-regular graphs with girth 3 or 4, 1, J. Combin. Theory, Ser. B, to appear."},{"key":"10.1016\/S0195-6698(87)80023-9_bib28","series-title":"Distance-regular graphs and generalisations, Ph.D. Thesis","author":"Terwilliger","year":"1982"},{"key":"10.1016\/S0195-6698(87)80023-9_bib29","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/0095-8956(83)90015-1","article-title":"Distance-regular graphs and (s","volume":"34","author":"Terwilliger","year":"1983","journal-title":"c, a, k)-graphs, J. Combin. Theory, Ser. B"},{"key":"10.1016\/S0195-6698(87)80023-9_bib30","unstructured":"P. Terwilliger: The Johnson graph J(d, n) is unique if (d, n) A (2, 8), preprint."},{"key":"10.1016\/S0195-6698(87)80023-9_bib31","doi-asserted-by":"crossref","first-page":"181","DOI":"10.32917\/hmj\/1206139234","article-title":"Composition of some series of association algebras","volume":"Ser. A-129","author":"Yamamoto","year":"1965","journal-title":"J. Sci. Hiroshima Univ."}],"container-title":["European Journal of Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0195669887800239?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0195669887800239?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,7,23]],"date-time":"2019-07-23T17:27:15Z","timestamp":1563902835000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0195669887800239"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,1]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1987,1]]}},"alternative-id":["S0195669887800239"],"URL":"https:\/\/doi.org\/10.1016\/s0195-6698(87)80023-9","relation":{},"ISSN":["0195-6698"],"issn-type":[{"value":"0195-6698","type":"print"}],"subject":[],"published":{"date-parts":[[1987,1]]}}}