# Characterization of power digraphs modulo $n$

Commentationes Mathematicae Universitatis Carolinae (2011)

- Volume: 52, Issue: 3, page 359-367
- ISSN: 0010-2628

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topAhmad, Uzma, and Husnine, Syed. "Characterization of power digraphs modulo $n$." Commentationes Mathematicae Universitatis Carolinae 52.3 (2011): 359-367. <http://eudml.org/doc/246164>.

@article{Ahmad2011,

abstract = {A power digraph modulo $n$, denoted by $G(n,k)$, is a directed graph with $Z_\{n\}=\lbrace 0,1,\dots , n-1\rbrace $ as the set of vertices and $E=\lbrace (a,b): a^\{k\}\equiv b\hspace\{4.44443pt\}(\@mod \; n)\rbrace $ as the edge set, where $n$ and $k$ are any positive integers. In this paper we find necessary and sufficient conditions on $n$ and $k$ such that the digraph $G(n,k)$ has at least one isolated fixed point. We also establish necessary and sufficient conditions on $n$ and $k$ such that the digraph $G(n,k)$ contains exactly two components. The primality of Fermat number is also discussed.},

author = {Ahmad, Uzma, Husnine, Syed},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {iteration digraph; isolated fixed points; Charmichael lambda function; Fermat numbers; Regular digraphs; iteration digraph; isolated fixed point; Fermat number; regular digraph},

language = {eng},

number = {3},

pages = {359-367},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Characterization of power digraphs modulo $n$},

url = {http://eudml.org/doc/246164},

volume = {52},

year = {2011},

}

TY - JOUR

AU - Ahmad, Uzma

AU - Husnine, Syed

TI - Characterization of power digraphs modulo $n$

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2011

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 52

IS - 3

SP - 359

EP - 367

AB - A power digraph modulo $n$, denoted by $G(n,k)$, is a directed graph with $Z_{n}=\lbrace 0,1,\dots , n-1\rbrace $ as the set of vertices and $E=\lbrace (a,b): a^{k}\equiv b\hspace{4.44443pt}(\@mod \; n)\rbrace $ as the edge set, where $n$ and $k$ are any positive integers. In this paper we find necessary and sufficient conditions on $n$ and $k$ such that the digraph $G(n,k)$ has at least one isolated fixed point. We also establish necessary and sufficient conditions on $n$ and $k$ such that the digraph $G(n,k)$ contains exactly two components. The primality of Fermat number is also discussed.

LA - eng

KW - iteration digraph; isolated fixed points; Charmichael lambda function; Fermat numbers; Regular digraphs; iteration digraph; isolated fixed point; Fermat number; regular digraph

UR - http://eudml.org/doc/246164

ER -

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