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.
