World Academy of Science, Engineering and Technology
Published March 5, 2016 | Version 10004380
Journal article Open

Hamiltonian Related Properties with and without Faults of the Dual-Cube Interconnection Network and Their Variations

Description

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.

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