Strongly regular fusions of tensor products of strongly regular graphs
type: Item
instance of: scholarly article
title: Strongly regular fusions of tensor products of strongly regular graphs
zbMATH Open document ID: 0813.05071
author: A. D. Sankey
published in: Rocky Mountain Journal of Mathematics
publication date: 1994-09-28T00:00:00Z
review text: Let \(G\) and \(H\) be strongly regular graphs with (0, 1)-adjacency matrices \(A_ 0= I\), \(A_ 1\), \(A_ 2= J-I- A_ 1\) and \(B_ 0= I\), \(B_ 1,\) \(B_ 2= J- I- B_ 1\) respectively. The tensor product \(G\otimes H\) is defined to be the nine class association scheme with adjacency matrices \(A_ i\otimes B_ j\). By combining (fusing) some of these nine classes, it is sometimes possible to obtain a third strongly regular graph \(F\). The main result of this paper is a complete classification of all parameter sets for strongly regular graphs \(G\), \(H\) and \(F\) for which such a fusion is possible.
Mathematics Subject Classification ID: 05E30
zbMATH DE Number: 645230
zbMATH Keywords: strongly regular graphs
zbMATH Keywords: tensor product
zbMATH Keywords: association scheme
zbMATH Keywords: adjacency matrices
zbMATH Keywords: fusion
reviewed by: Jack van Lint
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072428
OpenAlex ID: W2002029223
cites work: Subschemes of some association schemes
cites work: Q3218138
cites work: Q3863891
cites work: Coherent algebras
cites work: Strongly regular graphs
cites work: The Uniqueness of the $\mathrm{L}_2$ Association Scheme
DOI: 10.1216/RMJM/1181072428
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description: scientific article; zbMATH DE number 645230