The Wide Diameter of the Strong Product Graphs of Star Graphs and Cycles

Since graphs can represent the topology of a network, people often transform the topology of a network into a graph for analysis. The star network is a common computer network topology in which each device is directly connected to a central node, forming a star-shaped structure. The cycle network is also a common network topology. Furthermore, there exists a type of graph similar to star graphs, which is referred to as double star graphs. Therefore, the study of star graphs and cycles and double star graphs in graph theory is very extensive. Strong product is a commonly used method to construct a network. Using strong product to construct a network is not only convenient, but also preserves some good properties of factor graphs. Wide diameter is an important metric for measuring network transmission performance and reliability. This paper calculates the wide diameter of the networks constructed by the strong product between star graphs and cycles and between double star graphs and cycles.