Semi-regular relations and digraphs

Good strongly regular relations on weak $Gamma$-(semi)hypergroups

In this paper first we introduce the notion of weak $Gamma$-(semi)hypergroups, next some classes of equivalence relations which are called good regular and strongly good regular relations are defined.  Then we investigate some properties of this kind of relations on weak $Gamma$-(semi)hypergroups.

Classification of Regular Digraphs, Normally Regular Digraphs, and Strongly Regular Digraphs

We use an exhaustive generation with isomorph-rejection to classify three types of structured digraphs. The first type is the class of regular digraphs where each vertex has the same number of out-neighbors and inneighbors. The second type is the class of normally regular digraphs introduced by Jørgensen. In these digraphs, the number of common out-neighbors (or inneighbors) of vertices x and y...

Normally Regular Digraphs

A normally regular digraph with parameters (v, k, λ, μ) is a directed graph on v vertices whose adjacency matrix A satisfies the equation AAt = kI + λ(A + At) + μ(J − I − A − At). This means that every vertex has out-degree k, a pair of nonadjacent vertices have μ common out-neighbours, a pair of vertices connected by an edge in one direction have λ common out-neighbours and a pair of vertices ...

Weakly Distance-regular Digraphs

Exponents of 2-regular digraphs

A digraph G is called primitive if for some positive integer k, there is a walk of length exactly k from each vertex u to each vertex v (possibly u again). If G is primitive, the smallest such k is called the exponent of G, denoted by exp(G). A digraph G is said to be r-regular if each vertex in G has outdegree and indegree exactly r. It is proved that if G is a primitive 2-regular digraph with...