Strongly regular decompositions of the complete graph
type: Item
instance of: scholarly article
title: Strongly regular decompositions of the complete graph
zbMATH Open document ID: 1012.05161
DOI: 10.1023/A:1022939017002
published in: Journal of Algebraic Combinatorics
publication date: 2003-05-11T00:00:00Z
review text: In this paper several questions about amorphic association schemes and other strongly regular decompositions of the complete graph are studied, by investigating how two commuting edge-disjoint strongly regular graphs interact. A so-called amorphic association scheme has the property that all of its graphs are strongly regular. Moreover, they are all of Latin square type, or all of negative Latin square type. It is shown that any decomposition of the complete graph into three strongly regular graphs must be an amorphic association scheme. Likewise it is proved that any decomposition of the complete graph into strongly regular graphs of (negative) Latin square type is an amorphic association scheme. Strongly regular decompositions of the complete graph consisting of four graphs are studied, and a primitive counterexample to A. V. Ivanov's conjecture which states that any association scheme consisting of strongly regular graphs only must be amorphic is found.
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 1908577
zbMATH Keywords: amorphic association scheme
zbMATH Keywords: strongly regular graph
zbMATH Keywords: Latin square
author: Edwin R. Van Dam
reviewed by: Ioan Tomescu
MaRDI profile type: Publication
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full work available at URL: a:1022939017002
OpenAlex ID: W1604828720
description: scientific article; zbMATH DE number 1908577