Maximally Local-connected and Edge-bipancyclic Property with Conditional Faults on Interconnection Networks

• Main Authors: Shih, Lun-Min, 施倫閔
• Other Authors: Tan, Jimmy J.M.
• Format: Others
• Language: en_US
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/39257565332134096562

博士 === 國立交通大學 === 資訊科學與工程研究所 === 98 === The problem of fault-tolerance has been discussed widely. In this thesis, we study several properties with conditional fault on some interconnection networks. First of all, we show that for any set of faulty edges F of an n-dimensional hypercube Qn with F ≦2n-5, each edge of the faulty hypercube Qn -F lies on a cycle of every even length from 6 to 2n with each vertex having at least two healthy edges adjacent to it, for n≧3. Moreover, this result is optimal in the sense that there is a set F of 2n-4 conditional faulty edges in Qn such that Qn -F contains no Hamiltonian cycle. Second, we study the Menger property on a class of hypercube-like networks. We show that in all n-dimensional hypercube-like networks with n-2 vertices removed, every pair of unremoved vertices u and v are connected by min{deg(u),deg(v)} vertex-disjoint paths, where deg(u) and deg(v) are the remaining degree of vertices u and v, respectively. Furthermore, under the restricted condition that each vertex has at least two fault-free adjacent vertices, all hypercube-like networks still have the strong Menger property, even if there are up to 2n-5 vertex faults. The local connectivity of two vertices is defined as the maximum number of internally vertex-disjoint paths between them. Finally, we define two vertices to be maximally local-connected, if the maximum number of internally vertex-disjoint paths between them equals the minimum degree of these two vertices. We prove that a (k+1)-regular Matching Composition Network is maximally local-connected, even if there are at most (k-1) faulty vertices in it. Moreover, we introduce the one-to-many and many-to-many versions of connectivity, and prove that a (k+1)-regular Matching Composition Network is not only (k-1)-fault-tolerant one-to-many maximally local-connected but also f-fault-tolerant many-to-many t-connected (which will be defined subsequently) if f+t=2k. In the same issue, we show that an (n-1)-regular Cayley graph generated by transposition tree is maximally local-connected, even if there are at most (n-3) faulty vertices in it, and prove that it is also (n-1)-fault-tolerant one-to-many maximally local-connected.