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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 the problem of coherence of the network ad hoc of a problem of allocation
of frequency
We study a new class of graphs, the fatextended P4 graphs, and we give a polynomial time algorithm to
calculate the Grundy number of the graphs in this class. This result implies that the Grundy number can be
found in polynomial time for many graphs
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