{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,27]],"date-time":"2025-11-27T20:56:29Z","timestamp":1764276989901,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $\\Gamma$ denote a bipartite distance-regular graph with diameter $D$. In [Caughman (2004)], Caughman showed that if $D \\ge 12$, then $\\Gamma$ is $Q$-polynomial if and only if one of the following (i)-(iv) holds: (i) $\\Gamma$ is the ordinary $2D$-cycle, (ii) $\\Gamma$ is the Hamming cube $H(D,2)$, (iii) $\\Gamma$ is the antipodal quotient of the Hamming cube $H(2D,2)$, (iv) the intersection numbers of $\\Gamma$ satisfy $c_i = (q^i - 1)\/(q-1)$, $b_i = (q^D-q^i)\/(q-1)$ $(0 \\le i \\le D)$, where $q$ is an integer at least $2$. In this paper we show that the above result is true also for bipartite distance-regular graphs with $D \\in \\{9,10,11\\}$.<\/jats:p>","DOI":"10.37236\/7347","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:37:04Z","timestamp":1578670624000},"source":"Crossref","is-referenced-by-count":5,"title":["On Bipartite $Q$-Polynomial Distance-Regular Graphs with Diameter 9, 10, or 11"],"prefix":"10.37236","volume":"25","author":[{"given":"\u0160tefko","family":"Miklavi\u010d","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,3,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p52\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p52\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:37:46Z","timestamp":1579235866000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p52"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,2]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/7347","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,3,2]]},"article-number":"P1.52"}}