Spreads in Strongly Regular Graphs

Willem H. Haemers and Vladimir D. Tonchev
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Willem H. Haemers: Tilburg University
Vladimir D. Tonchev: Michigan Technological University

A chapter in Designs and Finite Geometries, 1996, pp 145-157 from Springer

Abstract: Abstract A spread of a strongly regular graph is a partition of the vertex set into cliques that meet Delsarte’s bound (also called Hoffman’s bound). Such spreads give rise to colorings meeting Hoffman’s lower bound for the chromatic number and to certain imprimitive three-class association schemes. These correspondences lead to conditions for existence. Most examples come from spreads and fans in (partial) geometries. We give other examples, including a spread in the McLaughlin graph. For strongly regular graphs related to regular two-graphs, spreads give lower bounds for the number of non-isomorphic strongly regular graphs in the switching class of the regular two-graph.

Keywords: strongly regular graphs; graph colorings; partial geometries; spreads; linked designs; regular 2-graphs (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-1395-3_10

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DOI: 10.1007/978-1-4613-1395-3_10

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