TY - JFULL AU - Jheng-Cheng Chen and Chia-Jui Lai and Chang-Hsiung Tsai and PY - 2010/5/ TI - A Systematic Approach for Finding Hamiltonian Cycles with a Prescribed Edge in Crossed Cubes T2 - International Journal of Computer and Information Engineering SP - 661 EP - 666 VL - 4 SN - 1307-6892 UR - https://publications.waset.org/pdf/3504 PU - World Academy of Science, Engineering and Technology NX - Open Science Index 40, 2010 N2 - 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. ER -