A local characterization of the Johnson scheme
type: Item
instance of: scholarly article
title: A local characterization of the Johnson scheme
zbMATH Open document ID: 0653.05019
DOI: 10.1007/BF02579203
published in: Combinatorica
publication date: 1987-01-01T00:00:00Z
review text: The Johnson scheme \({\mathcal J}(m,d)\) is the association scheme of all d- subsets of an m-set, the pair (x,y) of d-subsets in relation \({\mathcal J}_ i\), \(0\leq i\leq d\), provided \(| x\cap y| =d-i\). In this paper, within the Johnson scheme \({\mathcal J}(m,d)\) the graph K(m,d) of d-subsets of an m-set, two such adjacent when disjoint, is found. Among all connected graphs, K(m,d) is characterized by the isomorphism type of its vertex neighborhoods provided m is sufficiently large compared to d. The theorems find applications in the characterization of the Johnson scheme among the primitive association schemes and distance regular graphs.
Mathematics Subject Classification ID: 05B99
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 4065005
zbMATH Keywords: Johnson scheme
zbMATH Keywords: association scheme
zbMATH Keywords: distance regular graphs
author: J. I. Hall
reviewed by: Sanpei Kageyama
MaRDI profile type: Publication
cites work: Locally 4‐by‐4 grid graphs
cites work: Q3218140
cites work: Locally polar spaces and related rank 3 groups
cites work: On Identifying PG(3,2) and the Complete 3-Design on Seven Points
cites work: Locally cotriangular graphs
cites work: The graphs G(n,k) of the Johnson schemes are unique for n\(\geq 20\)
cites work: Characerization of a class of distance regular graphs.
cites work: Q3869375
full work available at URL: https://doi.org/10.1007/bf02579203
OpenAlex ID: W1964519767
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description: scientific article; zbMATH DE number 4065005