منابع مشابه
Directed Triple Systems
Directed triple systems are an example of block designs on directed graphs. A block design on a directed graph can be defined as follows. Let G be a directed graph of k vertices which contain no loops. Let S be a set of v elements. A collection of k-subsets of S with an assignment of the elements of each k-subset to the vertices of G is called a block design on G of order v if the following is ...
متن کاملMendelsohn directed triple systems
We introduce a class of ordered triple systems which are both Mendelsohn triple systems and directed triple systems. We call these Mendelsohn directed triple systems (MDTS(v, λ)), characterise them, and prove that they exist if and only if λ(v−1) ≡ 0 (mod 3). This is the same spectrum as that of regular directed triple systems, of which they are a special case. We also prove that cyclic MDTS(v,...
متن کاملPure Latin directed triple systems
It is well-known that, given a Steiner triple system, a quasigroup can be formed by defining an operation · by the identities x · x = x and x ·y = z where z is the third point in the block containing the pair {x, y}. The same is true for a Mendelsohn triple system where the pair (x, y) is considered to be ordered. But it is not true in general for directed triple systems. However directed tripl...
متن کاملClassification of Directed and Hybrid Triple Systems
Pairwise nonisomorphic directed and hybrid triple systems can be generated by, respectively, directing and ordering twofold triple systems and using the automorphisms of the twofold triple systems for isomorph rejection. Using this approach directed triple systems of order up to 10 and hybrid triple systems of order up to 9 are classified. In particular, it turns out that the number of nonisomo...
متن کاملSome bicyclic antiautomorphisms of directed triple systems
A transitive triple, (a, b, c), is defined to be the set {(a, b), (b, c), (a, c)} of ordered pairs. A directed triple system of order v, DTS(v), is a pair (D, β), where D is a set of v points and β is a collection of transitive triples of pairwise distinct points of D such that any ordered pair of distinct points of D is contained in precisely one transitive triple of β. An antiautomorphism of ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1973
ISSN: 0097-3165
DOI: 10.1016/0097-3165(73)90007-1