Embedding of Cycles in Arrangement Graphs

Arrangement graphs have been recently proposed as an attractive interconnection topology for large multiprocessor systems. In this correspondence, we further study these graphs by first proving the existence of Hamiltonian cycles in any arrangement graph. Secondly, we prove that an arrangement graph contains cycles of all lengths ranging between 3 and the size of the graph. Finally, we show that an arrangement graph can be decomposed into node disjoint cycles in many different ways.