Minimum and Maximum Strong Diameters of the Strong Product of Cycles and Paths

In interconnected networks, networks with smaller strong diameters tend to have better fault tolerance. This is because when the strong diameter of the network is small, the vertices are more closely connected and the path of information propagation is shorter, making it easier for the network to maintain communication and functionality in the event of an attack or failure. Whereas, when the strong diameter is large, the vertices are more distantly connected and the information propagation path is longer, which increases the vulnerability of the network and makes it more susceptible to attacks or failures. Therefore, strong diameter is one of the key metrics to measure and optimize the fault tolerance performance of the network. In this paper, a strong product network of cycles and paths is constructed by strong product and the strong diameter of this network is investigated. Specifically, we determine the minimum strong diameter of the strong product of even cycles and paths, and the upper and lower bounds of the minimum strong diameter of the strong product of odd cycles and paths. In addition, we give a lower bound on the maximum strong diameter of the strong product of cycles and paths, and present a conjecture on the maximum strong diameter of the strong product graph of cycles and paths.