A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is
On digraphs with unique walks of closed lengths between vertices
The Australasian Journal of Combinatorics
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 todblp:journals/ajc/Gimbert99 fatcat:27vmtgand5dwlbf35o2saowgla