Siamese Combinatorial Objects via Computer Algebra Experimentation

Mikhail Klin (), Sven Reichard () and Andrew Woldar ()
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Mikhail Klin: Ben-Gurion University of the Negev
Sven Reichard: University of Western Australia
Andrew Woldar: Villanova University

A chapter in Algorithmic Algebraic Combinatorics and Gröbner Bases, 2009, pp 67-112 from Springer

Abstract: Summary 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,q 2) 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.

Keywords: Color graph; Coherent configuration; Association scheme; Distance regular graph; Strongly regular graph; Generalized quadrangle; Spread; Steiner system; Siamese color graph; Siamese association scheme; Siamese Steiner design; Computer algebra package (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-01960-9_2

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DOI: 10.1007/978-3-642-01960-9_2

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