Hamiltonian-laceability of star graphs

Suppose G is a bipartite graph with two partite sets of equal size. G is said to be strongly hamiltonian-laceable if there is a hamiltonian path between every two vertices that belong to different partite sets, and there is a path of (maximal) length N-2 between every two vertices that belong to the same partite set, where N is the order of G. The star graph is known to be bipartite. In this paper, we show that the n-dimensional star graph, where n⩾4 is strongly hamiltonian-laceable