Learn More
A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. In this paper, we classify the s-regular elementary Abelian coverings of the three-dimensional hypercube for each s ≥ 1 whose fibre-preserving automorphism subgroups act arc-transitively. This gives a new infinite family of cubic 1-regular graphs, in which the smallest(More)
We introduce some constructions of weakly distance-regular digraphs of girth 2, and prove that a certain quotient digraph of a commutative weakly distance-transitive digraph of girth 2 is a distance-transitive graph. As an application of the result, we obtain some examples of weakly distance-regular digraphs which are not weakly distance-transitive.(More)
Let G be a connected graph and H be an arbitrary graph. In this paper, we study the identifying codes of the lexicographic product G[H] of G and H. We first introduce two parameters of H, which are closely related to identifying codes of H. Then we provide the sufficient and necessary condition for G[H] to be identifiable. Finally, if G[H] is identifiable,(More)