The crossed cube is a popular network topology because it possesses many attractive topological properties and its diameter is about half that of the hypercube. Typically, a network topology is modeled as a graph whose vertices and edges represent processors and communication links, respectively. We define a graph GG to be 22-disjoint-path-coverably rr-panconnected for a positive integer rr if for any four distinct vertices u,v,xu,v,x, and yy of GG, there exist two vertex-disjoint paths P1P1 and P2,P2, such that (i) P1P1 joins uu and vv with length ll for any integer ll satisfying r≤l≤|V(G)|−r−2r≤l≤|V(G)|−r−2, and (ii) P2P2 joins xx and yy with length |V(G)|−l−2|V(G)|−l−2, where |V(G)||V(G)| is the total number of vertices in GG. This property can be considered as an extension of both panconnectedness and connectivity. In this paper, we prove that the nn-dimensional crossed cube is 22-disjoint-path-coverably nn-panconnected.
關聯:
The Journal of Supercomputing July 2015, Volume 71, Issue 7, pp 2767–2782
