\r\nthe related studies and their variations are given. DCn was introduced

\r\nto be a network which retains the pleasing properties of hypercube Qn

\r\nbut has a much smaller diameter. In fact, it is so constructed that the

\r\nnumber of vertices of DCn is equal to the number of vertices of Q2n

\r\n+1. However, each vertex in DCn is adjacent to n + 1 neighbors and

\r\nso DCn has (n + 1) × 2^2n edges in total, which is roughly half the

\r\nnumber of edges of Q2n+1. In addition, the diameter of any DCn is 2n

\r\n+2, which is of the same order of that of Q2n+1. For selfcompleteness,

\r\nbasic definitions, construction rules and symbols are

\r\nprovided. We chronicle the results, where eleven significant theorems

\r\nare presented, and include some open problems at the end.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 112, 2016"}