We study the list homomorphism and retraction problems for the class of reflexive digraphs (digraphs in which each vertex has a loop). These problems have been intensively studied in the case of undirected graphs, but the situation seems more complex for digraphs. We also focus on an intermediate ‘subretraction’ problem. It turns out that the complexity of the subretraction problem can be class...

A digraph D is k-transitive if the existence of a directed path (v0, v1, . . . , vk), of length k implies that (v0, vk) ∈ A(D). Clearly, a 2-transitive digraph is a transitive digraph in the usual sense. Transitive digraphs have been characterized as compositions of complete digraphs on an acyclic transitive digraph. Also, strong 3 and 4-transitive digraphs have been characterized. In this work...

It is known that Moore digraphs of degree d and diameter k do not ex ist see or Furthermore for degree it is shown that for k there are no digraphs of order close to i e one less than Moore bound In this paper we shall consider digraphs of diameter k degree and number of vertices one less than Moore bound We give a necessary condition for the existence of such digraphs and using this condition ...

We classify the finite connected-homogeneous digraphs, as well as the infinite locally finite such digraphs with precisely one end. This completes the classification of all the locally finite connected-homogeneous digraphs.

In this paper, skew ABC matrix and its energy are introduced for digraphs. Firstly, some fundamental spectral features of the digraphs established. Then upper lower bounds presented Further extremal determined attaining these bounds.

We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related minimum distance diagrams. A dilating technique for these diagrams, which can be used for any degree of the digraph, is applied to generate the digraphs of the family. Moreover, two infinite families ...

In [19] Huang gave a characterization of local tournaments. His characterization involves arc-reversals and therefore may not be easily used to solve other structural problems on locally semicomplete digraphs (where one deals with a fixed locally semicomplete digraph). In this paper we derive a classification of locally semicomplete digraphs which is very useful for studying structural properti...

We call a digraph D = (V,E) a maximal m-free digraph if only if D has no cycles of length at most m and adding any ordered pair (u, v) 6∈ E will create a cycle of length at most m. In this note, we investigate this special class of digraphs. We will show that these digraphs share similar properties with tournament digraphs and this ”maximality” condition can be used to solve several extremal pr...

All weakly distance-regular digraphs with girth $2$ and k-k_{1,1}=1 are classified. A Family of Weakly Distance-Regular Digraphs of Girth 2 Kaishun Wang∗ School of Mathematical Sciences Beijing Normal University Beijing 100875, P.R. China Abstract All weakly distance-regular digraphs with girth 2 and k − k1,1 = 1 are classified.All weakly distance-regular digraphs with girth 2 and k − k1,1 = 1 ...