Two Edge-Disjoint Hamiltonian Cycles and One Isometric Path Cover in Augmented Cubes

• Main Authors: Chun-Kai Wang, 王俊凱
• Other Authors: Ruo-Wei Hung
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/10688943365551438099

碩士 === 朝陽科技大學 === 資訊工程系碩士班 === 100 === The n-dimensional hypercube network Qn is one of the most popular interconnection networks since it has simple structure and is easy to implement. The n-dimensional augmented cube AQn, an important variation of the hypercube, possesses several embedding properties that hypercubes and other variations do not possess. The advantages of AQn are that the diameter is only about half of the diameter of Qn and it is node-symmetric. Recently, some interesting properties of AQn have been investigated in the literature. The presence of edge-disjoint Hamiltonian cycles provides an advantage when implementing algorithms that require a ring structure by allowing message traffic to be spread evenly across the interconnection network. A network G contains one isometric path cover and is called isometric path coverable if for any two distinct pairs of nodes us, ut and vs, vt of G, there exist two node-disjoint paths P and Q satisfying that (1) P joins us and ut , and Q joins vs and vt , (2) |P| = |Q|, and (3) every node of G appears in P and Q exactly once. In this thesis, we first prove that the augmented cube AQn contains two edge-disjoint Hamiltonian cycles for n is equal or greater than 3. We then prove that AQn, with n is equal or greater than 2, is isometric path coverable. Based on the proofs of existences, we further present linear time algorithms to construct two edge-disjoint Hamiltonian cycles and one isometric path cover in an n-dimensional augmented cube AQn.