Vertex-primitive digraphs of prime-power order are hamiltonian

✍ Scribed by Ming-Yao Xu

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 158 KB
• Volume: 128
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(94)90134-1

✦ Synopsis

Witte proved that every connected Cayley digraph of a p-group is hamiltonian. In this note we generalize Witte's result to connected vertex-primitive digraphs of prime-power order; namely, we prove that every connected vertex-primitive digraph of prime-power order is hamiltonian. Witte [6] proved that every connected Cayley digraph of a p-group is hamiltonian. It is reasonable to attempt to generalize this result to vertex-transitive digraphs of prime-power order. The purpose of this note is to generalize Witte's result to the vertex-primitive case. First we give the following definition.

Definition. A digraph r is called vertex-primitive if its automorphism group Autr acts primitively on the vertex set V(T) of r.

The main result of this paper is the following group-theoretic theorem and its corollaries.