Optimal Radio Labeling for the Cartesian Product of Star and Even Circle

The graph itself can represent the topology of the network, so in the research of wireless communication network technology, graphs are often used to model the channel allocation of wireless communication networks. The distance between vertices of the graph is used to analyze the strength of channel interference between sites. In order to avoid interference and achieve interference interference-free communication, it is necessary to allocate channels reasonably in wireless communication. Radio labeling is a variant of the channel allocation problem, which transforms the channel allocation problem into a labeling problem of the graph. In this paper, by studying the Cartesian product topology of a star and an even cycle, we obtained the upper and lower bounds of their radio labeling.