Connectivity of some Algebraically Defined Digraphs

Authors

Aleksandr Kodess, University of Rhode IslandFollow
Felix Lazebnik

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_q, is defined as follows. The vertex of D is ��^l+1_q. There is an arc from a vertex x = (x1,...xl+1) to a vertex y = (y₁,...y_l+1) if x_i + y_i = f _i-l(x₁, y₁) 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