Displaying similar documents to “On a connection of number theory with graph theory”

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 iteration digraph and zero-divisor graph of the ring ℤ n

Tengxia Ju, Meiyun Wu (2014)

Czechoslovak Mathematical Journal

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In the first part, we assign to each positive integer n a digraph Γ ( n , 5 ) , whose set of vertices consists of elements of the ring ℤ n = { 0 , 1 , ⋯ , n - 1 } with the addition and the multiplication operations modulo n , and for which there is a directed edge from a to b if and only if a 5 ≡ b ( mod n ) . Associated with Γ ( n , 5 ) are two disjoint subdigraphs: Γ 1 ( n , 5 ) and Γ 2 ( n , 5 ) whose union is Γ ( n , 5 ) . The vertices of Γ 1 ( n , 5 ) are coprime to n , and the vertices of Γ 2 ( n , 5 ) are not coprime to n . In this part, we study the structure of Γ ( n , 5 ) in detail. In the second part, we investigate...