2-perfect Closed M-trail Systems of the Complete Directed Graph with Loops
نویسندگان
چکیده
Certain decompositions of complete directed graphs with loops into collections of closed trails which partition the edge set of the graph give rise to, and arise from, quasigroups. Such decompositions are said to be 2-perfect. The existence of these 2-perfect decompositions in which the closed trails are all of the same length m is examined. In particular, the set of values of n for which the order n complete directed graph with loops can be decomposed into 2-perfect closed trails of length m is determined (with four possible exceptions; two in the case m = 5 and two in the case m = 14) for all m :::; 15.
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عنوان ژورنال:
- Australasian J. Combinatorics
دوره 8 شماره
صفحات -
تاریخ انتشار 1993