%0 Journal Article
	%A Jheng-Cheng Chen and  Chia-Jui Lai and  Chang-Hsiung Tsai and 
	%D 2010
	%J International Journal of Computer and Information Engineering
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 40, 2010
	%T A Systematic Approach for Finding Hamiltonian Cycles with a Prescribed Edge in Crossed Cubes
	%U https://publications.waset.org/pdf/3504
	%V 40
	%X The crossed cube is one of the most notable variations of hypercube, but some properties of the former are superior to those of the latter. For example, the diameter of the crossed cube is almost the half of that of the hypercube. In this paper, we focus on the problem embedding a Hamiltonian cycle through an arbitrary given edge in the crossed cube. We give necessary and sufficient condition for determining whether a given permutation with n elements over Zn generates a Hamiltonian cycle pattern of the crossed cube. Moreover, we obtain a lower bound for the number of different Hamiltonian cycles passing through a given edge in an n-dimensional crossed cube. Our work extends some recently obtained results.

	%P 662 - 666