Optimal Radio Labeling of $C_{4}\boxtimes P_{n}$

The graph is generally used to model the channel allocation of wireless communication networks, and the distance parameter of the vertices in the graph is used to analyze the intensity of channel interference between radio stations. Channel allocation is the process of assigning appropriate channels to each station in the same network based on distance constraints to prevent the problem of interfering with each other's communications, and the concept of radio labeling is an emerging concept derived from converting the channel allocation problem into graph labeling problem. In this paper, we focus on the topology structure of the strong product of 4th order circle and nth order path (
$n\geq 7$
), and use it to simulate the channel allocation of a wireless communication network with the same structure. The consistency results of the upper and lower bounds of its radio labelings are obtained, and the optimal radio labeling is determined.