Abstract
Weakly distance-regular digraphs are digraphs with structures of association schemes. In this paper, we define a class of thin weakly distance-regular digraphs, and give its classification. For a finite group G and a generating subset S, let |x|S denote the minimum length l of an expression x=s1⋯sl with each si∈S. The classification of thin weakly distance-regular digraphs amounts to the determination of all finite groups G possessing a distinguished generating subset S that satisfies the following property:Forx,y∈G,(|x|S,|x−1|S)=(|y|S,|y−1|S)impliesx=y.As an application we also classify weakly distance-regular digraphs of out-degree two.
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