Siamese Combinatorial Objects via Computer Algebra Experimentation

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.

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