English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study $Q$-polynomial distance-regular graphs from the point of view ofwhat we call descendents, that is to say, those vertex subsets with theproperty 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 nontrivialdescendent with $w\ge 2$ is convex precisely when the graph has classicalparameters. The classification of descendents has been done for the 5 classicalfamilies of graphs associated with short regular semilattices. We revisit andcharacterize these families in terms of posets consisting of descendents, andextend the classification to all of the 15 known infinite families withclassical parameters and with unbounded diameter.

Vertex subsets with minimal width and dual width in $Q$-polynomial distance-regular graphs