Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is 3-transitive if the existence of the directed path (u, v, w, x) of length 3 in D implies the existence of the arc (u, x) ∈ A(D). In this article strong 3-transitive digraphs are characterized and the structure of non-strong 3-transitive digraphs is described. The results are used, e.g...

The theory of finitely supported structures is used for dealing with very large sets having a certain degree symmetry. This framework generalizes the classical set Zermelo-Fraenkel by allowing infinitely many basic elements no internal structure (atoms) and equipping group actions permutation over these elements. On other hand, soft represent generalization fuzzy to deal uncertainty in parametr...