The Wide Diameter of Strong Product Graphs of Complete Graphs and any Graphs

In large-scale interconnect networks, the properties of transmission delay and fault tolerance are highly valued. A good network should have low transmission delay and high fault tolerance regardless of whether it is a wired or wireless network. Due to the fact that the topology of a graph can represent the structure of actual interconnected networks, the study of graphs is crucial for the construction and evaluation of real networks. In order to measure these two properties of a network, the concept of wide diameter was introduced, which extends the concept of diameter of a graph. The wide diameter can measure the upper bound of a network's fault tolerance and transmission delay, and thus its study is necessary. By using the strong product method, it is possible to transform a small-scale wireless network into a large-scale wireless network, and possibly retained favorable properties. In this paper, we give the exact wide diameter of graphs constructed using the strong product of complete graphs and arbitrary graphs.