Optimal Radio Labeling of Cartesian Product of Wheel Graph and Cycle

Rapid advances in wireless communication have led to significant improvements in data transmission speeds, network coverage, and other aspects. However, the scarcity of spectrum resources presents a substantial challenge in modern network design. To address this issue, we transform the network frequency assignment problem into a graph vertex labeling and optimization problem. By introducing distance constraints on labeling and assigning unique labels to each site based on the spatial distribution of network nodes, we construct a spectrum assignment scheme that enhances the efficiency of spectrum management. This approach effectively improves the utilization of limited spectrum resources. In this paper, we focus on the radio labeling problem of the Cartesian product of the m-vertex wheel graph W_m and the n-vertex cycle C_n, where m≥ 3 and n≥ 4. By exploring the conditions satisfied by the radio labeling problem for such special graph, we present relevant theorems and examples. Corresponding comparative experiments are also provided to validate the effectiveness of the network model proposed in this paper.