#### Document Type

Article

#### Date of Original Version

2015

#### Abstract

Let *p *be a prime, *e* a positive integer, *q = p ^{e}*, and ��

_{q}

_{ }denote the finite field of

*q*elements. Let

*f*: ��

_{i}^{2}

_{q}→ ��

_{q}be arbitrary functions, where 1 ≤

*i*≤1,

*i*and

*l*are integers. The digraph

*D*=

*D*(

*q*:

**f**), where

**f**=

*f*,...,

*f*

_{l}): ��

^{2}

*→ ��*

_{q}^{l}

*, is defined as follows. The vertex of*

_{q}*D*is ��

^{l+1}

*. There is an arc from a vertex*

_{q}**x**= (x1,...xl+1) to a vertex

**y**= (

*y*,...

_{1}*y*

_{l}_{+1}) if

*x*+

_{i}*y*=

_{i}*f*-l(

_{i}*x*

_{1},

*y*

_{1}) for all

*i*, 2 ≤

*i*≤

*l*+ 1. In this paper we study the strong connectivity of

*D*and completely describe its strong components. The digraphs

*D*are directed analogues of some algebraically defined graphs, which have been studied extensively and have many applications.

#### Citation/Publisher Attribution

Kodess, A., & Lazebnik, F. (2015). Connectivity of some Algebraically Defined Digraphs. *Electronic Journal of Combinatorics, 22*(3), 1-11. Retrieved from https://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i3p27

Available at: https://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i3p27