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On digraphs with unique walks of closed lengths between vertices

1999
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The Australasian Journal of Combinatorics
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It is known that regular digraphs of degree d, diameter k and unique walks of length not smaller than h and not greater than k between all pairs of vertices ([ h, k ]-digraphs), exist only for h k and h = k 1, if d ;::: 2. This paper deals with the problem of the enumeration of [k -1, kJ-digraphs in the case of diameter k = 2 or degree d = 2. It is shown, using algebraic techniques, that the line digraph L K d + 1 of the complete digraph Kd+J is the only [1, 2]-digraph of degree d, that is to

dblp:journals/ajc/Gimbert99
fatcat:27vmtgand5dwlbf35o2saowgla