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Several authors modelled networks ad hoc by oriented or disoriented graphs,whereby the problem of allowance (allocation) of the frequencies at the levelof the network was transformed into coloring problem of nodes in the graph.Graph coloring is a tool to characterize the graphs. In our study, we wereinterested in particular in the coloring of vertex. In this domain, a largenumber of parameters of coloring were defined. A coloring for which twoneighboring summits do not have same color is called proper coloring. Weproposed to evaluate two other parameters vertex coloring maximizing the numberof colors to use: b-chromatic number and especially the number of Grundy. Thesestudies have focused on two types of graphs, which are the powers graphs andCartesian sum of graphs. In the first part, we determined borders among Grundyfor the Cartesian sum of graphs and finally we proposed algorithms for thecoloration of graphs. First of all, we gave some properties and results forsimple graphs (stable, chain, cycle, full, star, bipartisan). Secondly, westudied the Cartesian sum of two graphs by giving exact values of the number ofGrundy for diverse classes of graphs (sum of a chain and a chain, a chain and acycle, a cycle and a cycle) then we estimated borders of this parameter for thesum of a complete graph and any other graph. In the second part, we presentedthe results of the Cartesian sum of several graphs and in the last part; wealso gave an algorithm for generating graphs with a given number of Grundy.Thereafter, we studied another parameter namely the partial coloring Grundy.The properties of this parameter are close to those of total Grundy. Finally,we used parameters of coloring total Grundy and partial Grundy to generatealgorithms of coloring of graphs. We proposed algorithms of coloring basing onthe properties of certain graphs.

Algorithmes dynamiques pour la communication dans le r\'eseau ad hoc Coloration des graphes