Shih-Yan Chen and Shin-Shin Kao Hamiltonian Related Properties with and without Faults of the DualCube Interconnection Network and Their Variations
201 - 205
2016
10
4
International Journal of Mathematical and Computational Sciences http://waset.org/publications/10004380
http://waset.org/publications/112
World Academy of Science, Engineering and Technology
In this paper, a thorough review about dualcubes, 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) × 22n edges in total, which is roughly half the
number of edges of Q2n1. In addition, the diameter of any DCn is 2n
2, which is of the same order of that of Q2n1. 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.
International Science Index 112, 2016