Symmetric Digraphs from Powers Modulo n

Guixin Deng, Pingzhi Yuan

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DOI: 10.4236/ojdm.2011.13013                

Abstract

For each pair of positive integers n and k, let G(n,k) denote the digraph whose set of vertices is H = {0,1,2,···, n – 1} and there is a directed edge from a ∈ H to b ∈ H if a ≡ b(mod n). The digraph G(n,k) is symmetric if its connected component can be partitioned into isomorphic pairs. In this paper we obtain all symmetric G(n,k)

Keywords

Congruence, Digraph, Component, Height, Cycle

Conflicts of Interest

The authors declare no conflicts of interest.

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