Displaying similar documents to “Nonexistence of almost Moore digraphs of diameter three.”

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...

On a connection of number theory with graph theory

Lawrence Somer, Michal Křížek (2004)

Czechoslovak Mathematical Journal

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We assign to each positive integer n a digraph whose set of vertices is H = { 0 , 1 , ⋯ , n - 1 } and for which there is a directed edge from a ∈ H to b ∈ H if a 2 ≡ b ( m o d n ) . We establish necessary and sufficient conditions for the existence of isolated fixed points. We also examine when the digraph is semiregular. Moreover, we present simple conditions for the number of components and length of cycles. Two new necessary and sufficient conditions for the compositeness of Fermat numbers are also introduced.