The Johnson graph \(J(d,r)\) is unique if \((d,r)\neq (2,8)\)
type: Item
instance of: scholarly article
title: The Johnson graph \(J(d,r)\) is unique if \((d,r)\neq (2,8)\)
zbMATH Open document ID: 0587.05038
DOI: 10.1016/0012-365X(86)90160-3
published in: Discrete Mathematics
publication date: 1986-01-01T00:00:00Z
review text: For any positive integer \(r\) set \(S_r=\{1,2,\dots,r\}\). The Johnson graph \(J(d,r)\) \((2\leq 2d\leq r)\) is the graph whose vertex set consists of all subsets of \(S_r\) of order \(d\), with vertices adjacent if their intersection has order \(d-1\). The author proves that the Johnson graph \(J(d,r)\) is the unique distance-regular graph with its own intersection numbers if \((d,r)\neq (2,8)\).
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 3941578
zbMATH Keywords: Johnson graph
zbMATH Keywords: unique distance-regular graph
author: Paul Terwilliger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3941578