A digraph is a symmetric cycle if it is symmetric and its underlying graph is a cycle. It is proved that if D is an asymmetric digraph not containing a symmetric cycle, then D remains asymmetric after removing some vertex. It is also showed that each digraph D without a symmetric cycle, whose underlying graph is connected, contains a vertex which is a common fixed point of all automorphisms of D.

We characterise the primitive 2-closed groups G of rank at most four that are not automorphism group a graph or digraph and show if degree is least 2402 then there just two infinite families G⩽AΓL1(pd), 1-dimensional affine semilinear group. These first known examples non-regular digraph.

An acyclic decomposition of a digraph is a partition of the edges into acyclic subgraphs. Trivially every digraph has an acyclic decomposition into two subgraphs. It is proved that for every integer sX2 every digraph has an acyclic decomposition into s subgraphs such that in each subgraph the outdegree of each vertex v is at most degðvÞ s 1 l m : For all digraphs this degree bound is optimal. r...

This work introduces a novel topological constraint called the intopological digraph space imposed by subbasis ... contains one vertice such that edge ẹ is indegree of it and investigates some properties this structure. Our objective to provide crucial first step in study characteristics digraphs utilizing appropriate topology.

In this work, we design an algorithmic method to associate combinatorial structures with finite-dimensional Malcev algebras. In addition to its theoretical study, we have performed the implementation of procedures to construct the digraph associated with a given Malcev algebra (if its associated combinatorial structure is a digraph) and, conversely, a second procedure to test if a given digraph...

For any digraph D we construct a digraph s(S) such that D has a k-kernel iff s(S) has a k-kernel. The method employed allows to prove that, any digraph is an induced subdigraph of an infinite set of digraphs with (resp. without) k-kernel; and it can be used as a powerful tool in the construction of a large class of digraphs with (resp. without) k-kernel. Previous results are generalyzed. Mathem...