A remark on bipartite distance-regular graphs of even valency
type: Item
instance of: scholarly article
title: A remark on bipartite distance-regular graphs of even valency
zbMATH Open document ID: 0830.05063
DOI: 10.1007/BF01929483
author: Yanyan Li
published in: Graphs and Combinatorics
publication date: 1996-01-28T00:00:00Z
review text: Let \(\Gamma\) be a distance-regular graph with the intersection numbers \(p^s_{i,j}\), that is the number of vertices \(x\) with \(\delta(u, x)= i\) and \(\delta(v, x)= j\) for \(u, v\in \Gamma\) at distance \(s= \delta(u, v)\). The author establishes the following theorem: Given a bipartite distance-regular graph \(\Gamma\) with even valency \(b_0\) and \(t> 1\) the length of any series of \((1, 0, 1)\)'s in the intersection array modulo 2, then \(t+ 1\mid r_1+ 1\), with \(r_1\) the length of the first series and \(b_0= p^0_{1,1}\).
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 784143
zbMATH Keywords: distance-regular graph
zbMATH Keywords: intersection numbers
zbMATH Keywords: distance
zbMATH Keywords: valency
zbMATH Keywords: series
zbMATH Keywords: intersection array
reviewed by: Ulrich Knauer
MaRDI profile type: Publication
cites work: Q3992965
cites work: The diameter of bipartite distance-regular graphs
cites work: Distance-regular graphs and (s,c,a,k)-graphs
full work available at URL: https://doi.org/10.1007/bf01929483
OpenAlex ID: W1994305621
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description: scientific article; zbMATH DE number 784143