Optimal double-loop networks with non-unit steps.

Aguiló, F.; Simó, E.; Zaragozá, M.

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The paper extends the results given by M. Křížek and L. Somer, , Czech. Math. J. 54 (129) (2004), 465–485 (see [5]). For each positive integer $n$ define a digraph $Γ (n)$ whose set of vertices is the set $H = {0, 1, \dots, n - 1}$ and for which there is a directed edge from $a \in H$ to $b \in H$ if $a^{3} \equiv b (mod n) .$ The properties of such digraphs are considered. The necessary and the sufficient condition for the symmetry of a digraph $Γ (n)$ is proved. The formula for the number of fixed points of $Γ (n)$ is established. Moreover, some connection of the length...

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