Weakly distance-regular digraphs

Kaishun Wang, Hiroshi Suzuki
2003 Discrete Mathematics  
We consider the following generalization of distance-regular digraphs. A connected digraph is said to be weakly distance-regular if, for all vertices x and y with (@(x; y); @(y; x)) =h, |{z ∈ V | (@(x; z); @(z; x)) =ĩ and (@(z; y); @(y; z)) =j}| depends only onh;ĩ andj. We give some constructions of weakly distance-regular digraphs and discuss the connections to association schemes. Finally, we determine all commutative weakly distance-regular digraphs of valency 2.
doi:10.1016/s0012-365x(02)00562-9 fatcat:fgpx6rbewzghdleixavbk64ure