Optimizing distance constraints frequency assignment with relaxation

In a typical wireless telecommunication network, large number of communication links is established with limited available frequencies. The problem that addresses assigning frequencies to transmitters such interference avoided as far possible called the frequency assignment problem. usually modeled graph coloring (labeling) We study in this paper ( s , t )-relaxed L (2, 1)-labeling which considers situation where transceivers are very close receive differ by at least two while one. addition, model allows most (resp. ) anomalies distance one two). objective minimize span corresponding network. show it NP-complete decide whether minimal (1, 0)-relaxed k . also prove labeling for classes graphs bounded above square largest degree interest. These results confirm Conjecture 6 and partially 3 stated Lin [ J. Comb. Optim. 31 (2016) 1–22].