## Abstract

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.

Original language | English |
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Title of host publication | Algorithmic Algebraic Combinatorics and Gröbner Bases |

Publisher | Springer Berlin Heidelberg |

Pages | 67-112 |

Number of pages | 46 |

ISBN (Print) | 9783642019593 |

DOIs | |

State | Published - 1 Dec 2009 |

## Keywords

- 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)