Abstract
Our work becomes integrated into the general problem of the stability of the network ad hoc. Some, works attacked (affected) this problem. Among these works, we find the modelling of the network ad hoc in the form of a graph. We can resume theproblem of coherence of the network ad hocof a problem of allocation of frequency We study a new class of graphs, the fat-extended P4 graphs, and wegive a polynomial time algorithm to calculate the Grundy number of the graphs in thi s class. This result implies that the Grundy number can be found in polynomial time formany graphs
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