Non - Isomorphic 2 - Perfect 6 - Cycle Systems of Order 13
نویسنده
چکیده
It is known that necessary and sufficient conditions for the existence of a 2-perfect 6-cycle system of order n are that n = 1 or 9 mod 12 and n > 9 (Lindner, Phelps and Rodger [2]). Hence the smallest possible order of such a system is 13. The existence of a 2-perfect 6-cycle system of order 13 is shown by example in [2]. The example is cyclic. It is obvious that for large n the construction of a 2-perfect 6-cycle system of order n is not unique up to isomorphism but for small n such a result is not obvious. The most likely case for which uniqueness up to isomorphism might occur seemed to be 13 as it is the smallest possible order for such a system. However there is not a unique 2-perfect 6-cycle system of order 13; in fact the main result of this paper is:
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تاریخ انتشار 2008