Panpositionable hamiltonicity of the alternating group graphs

The alternating group graph AGn is an interconnection network topology based on the Cayley graph of the alternating group. There are some interesting results concerning the hamiltonicity and the fault tolerant hamiltonicity of the alternating group graphs. In this article, we propose a new concept called panpositionable hamiltonicity. A hamiltonian graph G is panpositionable if for any two different vertices x and y ofG and for any integer l satisfying d (x ,y ) ≤ l ≤ |V (G)| − d (x ,y ), there exists a hamiltonian cycle C of G such that the relative distance between x , y on C is l . We show that AGn is panpositionable hamiltonian if n ≥ 3. © 2007 Wiley Periodicals, Inc. NETWORKS, Vol. 50(2), 146–156 2007