Siamese combinatorial objects via computer algebra experimentation

Mikhail Klin, Sven Reichard, Andrew Woldar

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

4 Scopus citations


Following Kharaghani and Torabi [On a decomposition of complete graphs, Graphs Comb., 19 (2003), 519-526], we introduce new concepts of Siamese color graph, Siamese association scheme and Siamese Steiner design. With the aid of a computer, we determine all Siamese objects on 15 points, as well as hundreds on 40 points. As a generalization of accumulated observations, an infinite series of Siamese association schemes related to certain imprimitive actions of the groups PSL(2,q2) is outlined. Special attention is paid to the spirit of computer-aided activity, namely to algorithms, technical data, successful ad hoc tricks, and computer-free interpretations of obtained results.

Original languageEnglish
Title of host publicationAlgorithmic Algebraic Combinatorics and Gröbner Bases
PublisherSpringer Berlin Heidelberg
Number of pages46
ISBN (Print)9783642019593
StatePublished - 1 Dec 2009


  • Association scheme
  • Coherent configuration
  • Color graph
  • Computer algebra package
  • Distance regular graph
  • Generalized quadrangle
  • Siamese Steiner design
  • Siamese association scheme
  • Siamese color graph
  • Spread
  • Steiner system
  • Strongly regular graph

ASJC Scopus subject areas

  • Mathematics (all)


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