Complete Bipartite Networks Research Articles

Fault tolerant forwarding and optical indexes: A design theory approach

AbstractWe study the problem of designing fault tolerant routings in both complete and complete bipartite optical networks. We show that this problem has strong connections to various fundamental problems in design theory. Using a design theory approach, we find optimal f‐fault tolerant arc‐forwarding indexes for all complete networks and all complete balanced bipartite networks. Similarly, we find almost exact values for f‐fault tolerant optical indexes for these networks. © 2005 Wiley Periodicals, Inc. J Combin Designs

Synchronized clusters in coupled map networks. II. Stability analysis

We study self-organized and driven synchronization in some simple coupled map networks, namely globally coupled networks and complete bipartite networks, using both linear stability analysis and Lyapunov function approach and determine stability conditions for synchronization. The phase diagrams for the networks studied here have features very similar to the different kinds of structurally similar networks studied in Part I. Lyapunov function approach shows that when any two nodes are in driven synchronization, all the coupling terms in the difference between the variables of these two nodes cancel out, whereas when they are in self-organized synchronization, the direct coupling term between the two nodes adds an extra term while the other couplings cancel out. We also discuss the conditions for the occurrence of a floating node and suggest that the fluctuations of the conditional Lyapunov exponent about zero can be a criterion for its occurrence.

Optimal coteries and voting schemes

We consider coteries (i.e. intersecting, Sperner systems) on arbitrary networks with given node reliability, which maximize the network availability (i.e. the probability that the set of operating nodes has a connected subgraph which contains a set from the coterie). We show that the singleton coterie is always optimal on any network when the node reliability is p⩽ 1 2 . For p⩾ 1 2 , we give optimal coteries for the complete multipartite networks. The resulting optimal coteries when restricted to a special subclass of complete bipartite networks are shown to exceed the availability of any voting scheme, for p 1 2 .