Minimum Strong Radius of the Strong Product of Cycles and Even Paths
Shikun Zhou, Feng Li · 2024
In interconnection networks, the efficiency of information transmission depends on the length of the transmission path. Typically, we use radius as a metric to evaluate the information transmission performance of undirected networks; however, this metric is not applicable to directed networks. In a strongly directed graph, the strong distance between any two vertices is defined as the minimum directed strong subgraph of the strong directed graph containing these two vertices, the strong centrality of a vertex is defined as the maximum of the strong distances from that vertex to the other vertices, and the strong radius of the strong directed graph is defined as the minimum of the strong centrality of all the vertices. The minimum strong radius as the minimum of the strong radius of all strong directed graphs of the graph is an important metric for evaluating and optimizing the performance of information transmission in directed networks. In this paper, we construct a strong product network of cycles and even paths, and determine the exact value of the minimum strong radius of the strong product network of cycles and even paths when the length of the cycles is greater than or equal to 3 and greater than the length of the even paths. In addition, we give upper and lower bounds on the minimum strong radius of the strong product network of cycles and even paths when the length of the cycle is greater than or equal to 4 and less than or equal to the length of the even path.