Some implications on amorphic association schemes

E. R. van Dam, M. Muzychuk

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We give an overview of results on amorphic association schemes. We give the known constructions of such association schemes, and enumerate most such association schemes on up to 49 vertices. Special attention is paid to cyclotomic association schemes. We give several results on when a strongly regular decomposition of the complete graph is an amorphic association scheme. This includes a new proof of the result that a decomposition of the complete graph into three strongly regular graphs is an amorphic association scheme, and the new result that a strongly regular decomposition of the complete graph for which the union of any two relations is again strongly regular must be an amorphic association scheme.

Original languageEnglish
Pages (from-to)111-127
Number of pages17
JournalJournal of Combinatorial Theory - Series A
Volume117
Issue number2
DOIs
StatePublished - 1 Feb 2010
Externally publishedYes

Keywords

  • (Negative) Latin square type
  • Amorphic association scheme
  • Cyclotomic association scheme
  • Strongly regular decomposition
  • Strongly regular graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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