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)
Highlights
The digraph G(n,k) is symmetric if its connected components can be partitioned into isomorphic pairs
Hl Hi by Lemma 4.5, i l .We show that there are exactly ml components contained in G 2m, k h0
G n, k is symmetric if and only if k = 1 or k, m satisfy one of (i) - (v) in Theorem 3.1
Summary
In this paper we prove that if G n, k is symmetric, where k 2 and 2m n , m 5, k 4 or m, k satisfy one of the conditions of the above theorem. The outline of this paper is as follows.
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