Geodetically closed subgraphs in a distance-regular graph
type: Item
instance of: scholarly article
zbMATH Open document ID: 0986.05100
published in: Kyushu Journal of Mathematics
publication date: 2002-06-03T00:00:00Z
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 1702082
zbMATH Keywords: distance-regular graph
zbMATH Keywords: geodetically closed subgraph
author: Akira Hiraki
MaRDI profile type: Publication
full work available at URL: kyushujm.54.155
OpenAlex ID: W2133186926
DOI: 10.2206/KYUSHUJM.54.155
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title: Geodetically closed subgraphs in a distance-regular graph
review text: Let \(\Gamma\) be a distance-regular graph with \((c_1,b_1)=\cdots =(c_r,b_r)\neq (c_{r+1},b_{r+1})\), where \(r\geq 2\) and \(c_{r+1}>1\). Hiraki (1999) proved that either \(r=2\) or \((a_1,a_{r+1},c_{r+1}) =(0,0,2)\). The last case is consider in this paper. Theorem 1. Let \(\Gamma\) be a distance-regular graph of valency \(k\), \((c_1,b_1)=\cdots =(c_r,b_r)=(1,k-1)\) and \((c_{r+1},b_{r+1})=\cdots =(c_{2r},b_{2r}) =(2,k-2)\). Then \(r\leq 2\).
reviewed by: Alexandre A. Makhnev
description: scientific article; zbMATH DE number 1702082