Disjoint Hamilton cycles in the star graph

Abstract

In 1987, Akers, Harel and Krishnamurthy proposed the star graph Σ ( n ) as a new topology for interconnection networks. Hamiltonian properties of these graphs have been investigated by several authors. In this paper, we prove that Σ ( n ) contains ⌊ n / 8 ⌋ pairwise edge-disjoint Hamilton cycles when n is prime, and Ω ( n / log log n ) such cycles for arbitrary n.