Optimal Radio Labeling of Cartesian Product of Stars and Square Mesh Networks

The development of wireless communication technology has completely changed the way people communicate, from relying on fixed telephone lines in the past to today's anytime and anywhere interconnection, bringing unprecedented convenience. However, in the field of wireless communication, call quality is still facing a huge challenge, in which the degree of interference between channels is a key factor, and the limited channel resources are the main cause of interference in the network. The channel assignment problem in the network is transformed into the vertex labeling problem of the graph, and each vertex of the graph is assigned a unique label by the distance-label constraint. In this paper, we focus on the Cartesian product graphs of m-order square mesh networks and n-order stars (m, n > 3 and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m$</tex> is odd). We label the vertices of these Cartesian product graphs according to mathematical constraints, and determine the optimal value of their radio labels. The experimental data show that compared with the existing Cartesian product graph model of mesh networks and double stars, the topology designed in this paper is larger and the connectivity of the network is the highest, which has certain significance for the construction of large-scale wireless communication networks.