Zero Forcing Number of Optical Transpose Interconnection System Swapped Network

Abstract

An optical transpose interconnection system (OTIS) swapped network with 𝑛2 nodes is a two-level swapped architecture built by 𝑛 copies of an n-node basis network that constitutes its clusters. We explore the relations between basis network and optical transpose interconnection system (OTIS) swapped networks. We assume that the processor/nodes of the basis network are labeled [𝑛] = 1, . . . , 𝑛, and the processor or node labeled by 〈g, p〉 in OTIS network Ω identifies the node g in cluster p, and this corresponds to node 〈g, p〉 ∈ V(Ω). Subsequently, the cluster address of node 〈g, p〉 will be referred to as g, while the processor address will be referred to as 𝑝. In this thesis, our focus is on finding the zero-forcing number of OTIS swapped networks. Here, we show that the swapped connectivity actually introduces a desirable property that may not exist in the basis network. We construct OTIS swapped networks from the basis networks path, cycle, star, complete, wheel, fan and friendship and then find the zero forcing number of these OTIS swapped networks. We find new auxiliary for zero-forcing number of these graphs. We described that the zero-forcing number will be different for different graphs.