Minimum and Maximum Strong Diameter of the Strong Product of Complete Bipartite Graph and Path

Wireless networks typically focus on regular networks, and graph products serve as a key method to construct oriented regular networks. However, the purpose of designing oriented regular networks is to optimize their information transmission efficiency, so the strong diameter is a key parameter for evaluating networks' performance. A network with a smaller strong diameter enables lower latency and higher transmission efficiency even when communicating between the most distant pairs of vertex. Therefore, when optimizing network structures using method of graph products, controlling and reducing the network's strong diameter is the core task for enhancing its overall information transmission performance. In this paper, the minimum and maximum strong diameters of the strong product of $K_{m_1,m_2}\otimes P_n$ have been investigated, where $K_{m_1,m_2}$ and $P_n$ represent respectively complete bipartite graph and path. In addition, different strong orientation methods have been proposed to find the minimum and maximum strong diameters. Through comparative experiments, strong product networks are found to have a superior delay performance in information transmission when $m_1$ and $m_2$ are equal.