Displaying similar documents to “Optimal double-loop networks with non-unit steps.”

Properties of digraphs connected with some congruence relations

J. Skowronek-Kaziów (2009)

Czechoslovak Mathematical Journal

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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 , , n - 1 } and for which there is a directed edge from a H to b H if a 3 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...