Vertex subsets with minimal width and dual width in \(Q\)-polynomial distance-regular graphs
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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.
DOI :
10.37236/654
Classification :
05E30, 05C50, 05C12, 06A06, 06A12, 05C75
Mots-clés : descendents, short regular semilattices
Mots-clés : descendents, short regular semilattices
@article{10_37236_654,
author = {Hajime Tanaka},
title = {Vertex subsets with minimal width and dual width in {\(Q\)-polynomial} distance-regular graphs},
journal = {The electronic journal of combinatorics},
year = {2011},
volume = {18},
number = {1},
doi = {10.37236/654},
zbl = {1235.05160},
url = {http://geodesic.mathdoc.fr/articles/10.37236/654/}
}
Hajime Tanaka. Vertex subsets with minimal width and dual width in \(Q\)-polynomial distance-regular graphs. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/654
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