Displaying similar documents to “Balanced path decomposition of λ K n , n and λ K n , n * ”

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...

Decomposition of Complete Bipartite Multigraphs Into Paths and Cycles Having k Edges

Shanmugasundaram Jeevadoss, Appu Muthusamy (2015)

Discussiones Mathematicae Graph Theory

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We give necessary and sufficient conditions for the decomposition of complete bipartite multigraph Km,n(λ) into paths and cycles having k edges. In particular, we show that such decomposition exists in Km,n(λ), when λ ≡ 0 (mod 2), [...] and k(p + q) = 2mn for k ≡ 0 (mod 2) and also when λ ≥ 3, λm ≡ λn ≡ 0(mod 2), k(p + q) =λ_mn, m, n ≥ k, (resp., m, n ≥ 3k/2) for k ≡ 0(mod 4) (respectively, for k ≡ 2(mod 4)). In fact, the necessary conditions given above are also sufficient when λ =...

The cubic mapping graph for the ring of Gaussian integers modulo n

Yangjiang Wei, Jizhu Nan, Gaohua Tang (2011)

Czechoslovak Mathematical Journal

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The article studies the cubic mapping graph Γ ( n ) of ℤ n [ i ] , the ring of Gaussian integers modulo n . For each positive integer n > 1 , the number of fixed points and the in-degree of the elements 1 ¯ and 0 ¯ in Γ ( n ) are found. Moreover, complete characterizations in terms of n are given in which Γ 2 ( n ) is semiregular, where Γ 2 ( n ) is induced by all the zero-divisors of ℤ n [ i ] .