Recently an operation of graphs called substitution has been incorporated. In an informal way, the substitution consists in the replacement of a vertex for a graph. This new graph is characterized through a function (of substitution) that it could be self definable. The substitution of each vertex of a graph G, through injectives functions of substitution, by the same G graph will be called autosubstitution and denoted by G(G). If X represents the class of all the simple and finite graphs and w is an application of X in X, defined by w (G) = G (G), then it is interest in studying the dynamic properties of w and the construction of some algorithms that they permit the generating of fractal images. In function of the above-mentioned it is proposed to analyze the autosubstitution for graphs simple and finite. Framed in the area of the Graph Dynamics, inside the area of the Graph Theory, the present work will use, preferably, simple and finite graph