Optimal Radio Labeling of the Cylindrical Gird Network with Fan Subgraph

With the rapid development of wireless communication networks, the frequency assignment problem for wireless networks has been transformed into a graph labeling problem: specifically, each base station is represented by a vertex in an undirected graph, and vertices that may cause interference are connected by edges, with adjacent vertices unable to use the same frequency. However, determining the frequency assignment for an arbitrary graph is an NP-hard problem. Therefore, based on an exploration of grid network models, this paper focuses on the labeling problem of the cylindrical gird network with fan subgraph model [Formula: see text] where [Formula: see text] and [Formula: see text], that is, the Cartesian product of the [Formula: see text]-order fan graph and the [Formula: see text]-order cycle. First, we present lower bounds of radio labeling and several results for this class of network models. Second, we label the vertices of this special graph and determine the optimal number. Finally, through numerical comparisons and application examples, experimental data demonstrate that compared to existing Cartesian product models of cycle and cycle, complete graph and cycle, the topological model designed in this paper has higher optimization under the same number of vertices. Specifically, the Cartesian product model of the fan graph and cycle requires fewer radio labelings.