%0 Journal Article
	%A Shih-Yan Chen and  Shin-Shin Kao
	%D 2016
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 112, 2016
	%T Hamiltonian Related Properties with and without Faults of the Dual-Cube Interconnection Network and Their Variations
	%U https://publications.waset.org/pdf/10004380
	%V 112
	%X 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.
	%P 201 - 205