We define G(n, k) to be a directed graph whose set of vertices is {0, 1, ..., n−1} and whose set of edges is defined by a modular relation. We say that G(n, k) is symmetric of order m if we can partition G(n, k) into subgraphs, each containing m components, such that all the components in a subgraph are isomorphic. We develop necessary and sufficient conditions for G(n, k) to contain symmetry when n is odd and square-free. Additionally, we use group theory to describe the structural properties of the subgraph of G(n, k) containing only those vertices relatively prime to n
AbstractWe assign to each positive integer n a digraph G(n) whose set of vertices is H={0,1,…,n-1} a...
summary:A power digraph, denoted by $G(n,k)$, is a directed graph with $\mathbb Z_{n}=\{0,1,\dots ,...
summary:We assign to each positive integer $n$ a digraph whose set of vertices is $H=\lbrace 0,1,\do...
We define G(n, k) to be a directed graph whose set of vertices is {0, 1,..., n − 1} and whose set of...
AbstractFor any positive integers n and k, let G(n,k) denote the digraph whose set of vertices is H=...
For each pair of positive integers n and k, let G(n,k) denote the digraph whose set of vertices is H...
summary:A power digraph modulo $n$, denoted by $G(n,k)$, is a directed graph with $Z_{n}=\{0,1,\dots...
AbstractWe assign to each pair of positive integers n and k≥2 a digraph G(n,k) whose set of vertices...
The modular exponentiation is considered to be one of the renowned problems in number theory and is ...
summary:The paper extends the results given by M. Křížek and L. Somer, {\it On a connection of numbe...
summary:Let $p$ be a prime. We assign to each positive number $k$ a digraph $G_{p}^{k}$ whose set of...
For positive integers n and k, let G(n,k) denote the digraph whose set of vertices is {0,1,2,…,n-1} ...
AbstractIt is proved that if p is a prime, k and m⩽p are positive integers, and I is a vertex symmet...
summary:For any two positive integers $n$ and $k \geq 2$, let $G(n,k)$ be a digraph whose set of ver...
summary:We assign to each pair of positive integers $n$ and $k\ge 2$ a digraph $G(n,k)$ whose set o...
AbstractWe assign to each positive integer n a digraph G(n) whose set of vertices is H={0,1,…,n-1} a...
summary:A power digraph, denoted by $G(n,k)$, is a directed graph with $\mathbb Z_{n}=\{0,1,\dots ,...
summary:We assign to each positive integer $n$ a digraph whose set of vertices is $H=\lbrace 0,1,\do...
We define G(n, k) to be a directed graph whose set of vertices is {0, 1,..., n − 1} and whose set of...
AbstractFor any positive integers n and k, let G(n,k) denote the digraph whose set of vertices is H=...
For each pair of positive integers n and k, let G(n,k) denote the digraph whose set of vertices is H...
summary:A power digraph modulo $n$, denoted by $G(n,k)$, is a directed graph with $Z_{n}=\{0,1,\dots...
AbstractWe assign to each pair of positive integers n and k≥2 a digraph G(n,k) whose set of vertices...
The modular exponentiation is considered to be one of the renowned problems in number theory and is ...
summary:The paper extends the results given by M. Křížek and L. Somer, {\it On a connection of numbe...
summary:Let $p$ be a prime. We assign to each positive number $k$ a digraph $G_{p}^{k}$ whose set of...
For positive integers n and k, let G(n,k) denote the digraph whose set of vertices is {0,1,2,…,n-1} ...
AbstractIt is proved that if p is a prime, k and m⩽p are positive integers, and I is a vertex symmet...
summary:For any two positive integers $n$ and $k \geq 2$, let $G(n,k)$ be a digraph whose set of ver...
summary:We assign to each pair of positive integers $n$ and $k\ge 2$ a digraph $G(n,k)$ whose set o...
AbstractWe assign to each positive integer n a digraph G(n) whose set of vertices is H={0,1,…,n-1} a...
summary:A power digraph, denoted by $G(n,k)$, is a directed graph with $\mathbb Z_{n}=\{0,1,\dots ,...
summary:We assign to each positive integer $n$ a digraph whose set of vertices is $H=\lbrace 0,1,\do...