Balanced path decomposition of $\lambda K_{n,n}$ and $\lambda K^*_{n,n}$

Hung-Chih Lee; Chiang Lin

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 $ℤ_{n} = {0, 1, \dots, n - 1}$ 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 $a^{5} \equiv b (mod n)$ . 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 =...

Heights in finite projective space, and a problem on directed graphs.

Nathanson, Melvyn B., Sullivan, Blair D. (2008)

Integers

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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 $\bar{1}$ and $\bar{0}$ 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 $ℤ_{n} [i]$ .

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

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

Heights in finite projective space, and a problem on directed graphs.

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

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 $ℤ_{n}$

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