Distance-regularised graphs are distance-regular or distance-biregular
type: Item
instance of: scholarly article
title: Distance-regularised graphs are distance-regular or distance-biregular
zbMATH Open document ID: 0616.05041
DOI: 10.1016/0095-8956(87)90027-X
author: John Shawe-Taylor
author: Chris Godsil
published in: Journal of Combinatorial Theory. Series B
publication date: 1987-01-01T00:00:00Z
review text: The authors are concerned that the theory of distance-regular graphs does not apply directly to the graphs of generalised polygons. They therefore define a distance-regularised graph to be one in which, for any integer k and any vertices x and y, the number of vertices at distance k from x and adjacent to y only depends on the vertex x and the distance between x and y. It is then shown that te nonbipartite distance regularised graphs are distance regular, while the bipartite ones are distance-biregular. Much of the theory of distance-regular graphs is extended to distinct- regularised graphs. Apart from the generalised polygons, three classes of distance-biregular graphs are given. The question of whether these are all the distance biregular graphs remains open.
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 3997835
zbMATH Keywords: distance-regular graphs
zbMATH Keywords: distance-regularised graph
zbMATH Keywords: distance-biregular
MaRDI profile type: Publication
cites work: Q4770409
cites work: Spectral conditions for the reconstructibility of a graph
cites work: Distance-biregular graphs with 2-valent vertices and distance regular line graphs
cites work: Automorphism groups of primitive distance-bitransitive graphs are almost simple
cites work: Generalized n-gons and Chebyshev polynomials
full work available at URL: 0095-8956(87)90027-x
OpenAlex ID: W2012945176
description: scientific article; zbMATH DE number 3997835