Cycle-balance conditions for distance-regular graphs
type: Item
instance of: scholarly article
title: Cycle-balance conditions for distance-regular graphs
zbMATH Open document ID: 1017.05105
DOI: 10.1016/S0012-365X(02)00557-5
author: Aaron D. Meyerowitz
published in: Discrete Mathematics
publication date: 2003-04-09T00:00:00Z
review text: It is known that in a distance-regular graph, the partition with respect to the distance from a vertex supports a unique eigenvector for each eigenvalue. There may be non-singleton vertex sets whose corresponding distance partition also supports eigenvectors. In this paper, the members of three families of distance-regular graphs, viz. the John graphs, Hamming graphs, and complete multipartite graphs have been considered. For each, all such sets which support an eigenvector for the next to the largest eigenvalue have been determined. These sets exhibit the underlying geometric structure of the graph.
reviewed by: Bai Kishan Dass
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 1896029
zbMATH Keywords: distance-regular graph
zbMATH Keywords: vertex partition
zbMATH Keywords: geometry
zbMATH Keywords: eigenvector
zbMATH Keywords: eigenvalue
MaRDI profile type: Publication
full work available at URL: s0012-365x(02)00557-5
OpenAlex ID: W2140115032
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description: scientific article; zbMATH DE number 1896029