Uniqueness of strongly regular graphs having minimal \(p\)-rank
type: Item
instance of: scholarly article
title: Uniqueness of strongly regular graphs having minimal \(p\)-rank
zbMATH Open document ID: 0831.05066
DOI: 10.1016/0024-3795(95)00184-S
author: René Peeters
published in: Linear Algebra and its Applications
publication date: 1996-02-12T00:00:00Z
review text: Let \(\Gamma\) be a strongly regular graph with adjacency matrix \(A\). Let \(I\) be the identity matrix and let \(p\) be a prime. We study the \(p\)-ranks of the matrices \(A + cI\) for integral \(c\) and want to characterize among all strongly regular graphs with a given parameter set those for which a \(p\)-rank is minimal. After mentioning which \(p\)-ranks of a strongly regular graph are not determined by these parameters we use these relevant \(p\)-ranks as extra parameters to characterize strongly regular graphs. Four classes of strongly regular graphs are discussed: Paley graphs, latin square graphs, symplectic graphs and collinearity graphs of generalized quadrangles with four points per line.
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 51E12
Mathematics Subject Classification ID: 05B07
zbMATH DE Number: 803726
zbMATH Keywords: \(p\)-rank
zbMATH Keywords: strongly regular graph
zbMATH Keywords: adjacency matrix
zbMATH Keywords: Paley graphs
zbMATH Keywords: latin square graphs
zbMATH Keywords: symplectic graphs
zbMATH Keywords: collinearity graphs
zbMATH Keywords: generalized quadrangles
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 803726