The Radio Number of Cartesian Product for Stars and Square Mesh Networks

As the most critical component in the communication process, channels have a great impact on the communication quality of network and telephone. With the continuous expansion of network scale, the limited channel resources lead to the limitation of communication network scale. Therefore, achieving reasonable channel assignment and utilization becomes an extremely challenging problem. In order to solve this problem effectively, the channel assignment problem in communication networks can be transformed into a graph labeling problem, utilizing graphs with the same topology as the network to simulate the communication network. In this paper, the topologies of Cartesian product of mesh and star networks are studied. The lower bound and exact value of the radio number of the Cartesian product of square mesh network and star G = P(m,m)□K<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1,n</inf> are determined, where m ≥ 4 and is even.