{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T07:24:12Z","timestamp":1778657052267,"version":"3.51.4"},"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>We study $Q$-polynomial distance-regular graphs from the point of view of what we call descendents, that is to say, those vertex subsets with the property that the width $w$ and dual width $w^*$ satisfy $w+w^*=d$, where $d$ is the diameter of the graph. We show among other results that a nontrivial descendent with $w\\geq 2$ is convex precisely when the graph has classical parameters. The classification of descendents has been done for the $5$ classical families of graphs associated with short regular semilattices. We revisit and characterize these families in terms of posets consisting of descendents, and extend the classification to all of the $15$ known infinite families with classical parameters and with unbounded diameter.<\/jats:p>","DOI":"10.37236\/654","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:43:02Z","timestamp":1578714182000},"source":"Crossref","is-referenced-by-count":7,"title":["Vertex Subsets with Minimal Width and Dual Width in $Q$-Polynomial Distance-Regular Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"Hajime","family":"Tanaka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,8,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p167\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p167\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:07:02Z","timestamp":1579302422000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p167"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,8,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/654","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,8,19]]},"article-number":"P167"}}