@article{(Open Science Index):https://publications.waset.org/pdf/10004380, title = {Hamiltonian Related Properties with and without Faults of the Dual-Cube Interconnection Network and Their Variations}, author = {Shih-Yan Chen and Shin-Shin Kao}, country = {}, institution = {}, abstract = {In this paper, a thorough review about dual-cubes, DCn, the related studies and their variations are given. DCn was introduced to be a network which retains the pleasing properties of hypercube Qn but has a much smaller diameter. In fact, it is so constructed that the number of vertices of DCn is equal to the number of vertices of Q2n +1. However, each vertex in DCn is adjacent to n + 1 neighbors and so DCn has (n + 1) × 2^2n edges in total, which is roughly half the number of edges of Q2n+1. In addition, the diameter of any DCn is 2n +2, which is of the same order of that of Q2n+1. For selfcompleteness, basic definitions, construction rules and symbols are provided. We chronicle the results, where eleven significant theorems are presented, and include some open problems at the end.}, journal = {International Journal of Mathematical and Computational Sciences}, volume = {10}, number = {4}, year = {2016}, pages = {201 - 205}, ee = {https://publications.waset.org/pdf/10004380}, url = {https://publications.waset.org/vol/112}, bibsource = {https://publications.waset.org/}, issn = {eISSN: 1307-6892}, publisher = {World Academy of Science, Engineering and Technology}, index = {Open Science Index 112, 2016}, }