On the heights of power digraphs modulo $n$

Uzma Ahmad; Husnine Syed

Displaying similar documents to “On the heights of power digraphs modulo $n$ ”

The structure of digraphs associated with the congruence $x^{k} \equiv y (mod n)$

Lawrence Somer, Michal Křížek (2011)

Czechoslovak Mathematical Journal

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We assign to each pair of positive integers $n$ and $k \geq 2$ a digraph $G (n, k)$ whose set of vertices is $H = {0, 1, \dots, n - 1}$ and for which there is a directed edge from $a \in H$ to $b \in H$ if $a^{k} \equiv b (mod n)$ . We investigate the structure of $G (n, k)$ . In particular, upper bounds are given for the longest cycle in $G (n, k)$ . We find subdigraphs of $G (n, k)$ , called fundamental constituents of $G (n, k)$ , for which all trees attached to cycle vertices are isomorphic.

Isomorphic digraphs from powers modulo $p$

Guixin Deng, Pingzhi Yuan (2011)

Czechoslovak Mathematical Journal

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Let $p$ be a prime. We assign to each positive number $k$ a digraph $G_{p}^{k}$ whose set of vertices is ${1, 2, ..., p - 1}$ and there exists a directed edge from a vertex $a$ to a vertex $b$ if $a^{k} \equiv b (mod p)$ . In this paper we obtain a necessary and sufficient condition for $G_{p}^{k_{1}} ≃ G_{p}^{k_{2}}$ .

On semiregular digraphs of the congruence $x^{k} \equiv y (mod n)$

Lawrence Somer, Michal Křížek (2007)

Commentationes Mathematicae Universitatis Carolinae

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We assign to each pair of positive integers $n$ and $k \geq 2$ a digraph $G (n, k)$ whose set of vertices is $H = {0, 1, \dots, n - 1}$ and for which there is a directed edge from $a \in H$ to $b \in H$ if $a^{k} \equiv b (mod n)$ . The digraph $G (n, k)$ is semiregular if there exists a positive integer $d$ such that each vertex of the digraph has indegree $d$ or 0. Generalizing earlier results of the authors for the case in which $k = 2$ , we characterize all semiregular digraphs $G (n, k)$ when $k \geq 2$ is arbitrary.

Displaying similar documents to “On the heights of power digraphs modulo n ”

The structure of digraphs associated with the congruence x k ≡ y ( mod n )

Isomorphic digraphs from powers modulo p

On semiregular digraphs of the congruence x k ≡ y ( mod n )

Displaying similar documents to “On the heights of power digraphs modulo $n$ ”

The structure of digraphs associated with the congruence $x^{k} \equiv y (mod n)$

Isomorphic digraphs from powers modulo $p$

On semiregular digraphs of the congruence $x^{k} \equiv y (mod n)$