Weakly Distance-Regular Digraphs of Valency Three, I

Weakly Distance-Regular Digraphs of Valency Three, I

Suzuki (2004) classified thin weakly distance-regular digraphs and proposed the project to classify weakly distance-regular digraphs of valency 3. The case of girth 2 was classified by the third author (2004) under the assumption of the commutativity. In this paper, we continue this project and classify these digraphs with girth more than 2 and two types of arcs.

Weakly Distance-regular Digraphs

Weakly Distance-Regular Digraphs of Girth 2

In this paper, we give two constructions of weakly distance-regular digraphs of girth 2, and prove that certain quotient digraph of a commutative weakly distancetransitive digraph of girth 2 is a distance-transitive graph. As an application of the result, we not only give some constructions of weakly distance-regular digraphs which are not weakly distance-transitive, but determine a special cla...

A family of weakly distance-regular digraphs of girth 2

All weakly distance-regular digraphs with girth 2 and k − k1,1 = 1 are determined. Moreover, all such digraphs are commutative.

Title : A Family of Weakly Distance - Regular Digraphs of Girth

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 ...