### ATTRACTORS POINTS IN THE

AUTOSUBSTITUTION^{*}

*EDUARDO MONTENEGRO Universidad Técnica FedericoSanta María, Chile and EDUARDO CABRERA Universidad de Playa Ancha, Valparaíso - Chile *

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**Abstract**

*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.*

**Key words : ***Graph, subtitution of graph, discrete dynamical systems.*

**AMS subject classifications : ***05C25 ; 05C35*

* Work financed by the General Address of Investigation of the UPLACED trougth the Project CNEI 060001.

**REFERENCES**

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Received : May, 2000

**Eduardo Montenegro**

Instituto de Matemáticas

Universidad Católica de Valparaíso

Blanco Viel N 596

Cerro Baron

Valparaíso

Chile ]]> e-mail : emontenv@ucv.cl

and

**Eduardo Cabrera**

Facultad de Ciencias Naturales y Exactas

Universidad de Playa Ancha

Casilla 34-V

Valparaíso

Chile

e- mail : emontene@upa.cl ]]>