Minimum Strong Radius of the Strong Product of Cycles and Odd Paths

In the Internet, the effectiveness of information transmission depends directly on the transmission path. Determining the shortest transmission path is the core element to improve the efficiency of information transmission. The minimum strong radius, as an important parameter for measuring the shortest directed path in directed networks, becomes a key criterion for evaluating the performance of information transmission in the Internet. In this paper, we utilize the strong product of graphs to construct large-scale networks by using cycles and paths as factor graphs. By analyzing the relationship between the topological parameters of these factor graphs, we determine the exact value of the minimum strong radius of the strong product of cycles and odd paths under $m\gt n\geq 3$. In addition, we give upper and lower bounds on the minimum strong radius in the $3\leq m\gt n$ and $m=n\geq 4$ cases.