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Let p be a prime, e a positive integer, q = pe, and 𝔽q denote the finite field of q elements. Let fi : 𝔽2q → 𝔽q be arbitrary functions, where 1 ≤ i ≤1, i and l are integers. The digraph D = D(q:f), where f = f ,..., f l): 𝔽2q → 𝔽lq, is defined as follows. The vertex of D is 𝔽l+1q. There is an arc from a vertex x = (x1,...xl+1) to a vertex y = (y1,...yl+1) if xi + yi = 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.
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