Attractors points in the autosubstitution

Authors

  • Eduardo Montenegro Universidad Católica de Valparaíso.
  • Eduardo Cabrera Universidad de Playa Ancha.

DOI:

https://doi.org/10.4067/S0716-09172001000200004

Keywords:

Graph, Substitution of graph, Discrete dynamical systems.

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 fi- nite 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.

Author Biographies

Eduardo Montenegro, Universidad Católica de Valparaíso.

Instituto de Matemáticas.

Eduardo Cabrera, Universidad de Playa Ancha.

Facultad de Ciencias Naturales y Exactas.

References

[1] M. BARNSLEY, Fractal Everywhere, Academic Press, (1988).

[2] A. BRONDSTED, An Introduction to Convex Polytopes, Springer Verlag, New York, Heidelberg, Berlin, (1983).

[3] G. CHARTRAND, LESNIAIK, L., Graphs and Digraphs, Wadsworth and Brooks/Cole Advanced Books and Software Pacific Grove, C. A., (1996).

[4] G. CHARTRAND AND O. OELLERMANN, Applied and Algorithmic Graph Theory, McGraw-Hill., Inc., (1993).

[5] H. COXETER, Regular Polytopes, Third Edition, Dover Publication, Inc, (1973).

[6] R. DEVANEY, Introduction to Chaotic Dynamical Systems, 2nd edition, Addison-Wesley, (1989).

[7] R. HOLMGREN, A First Course in Discrete Dynamical Systems, Springer-Verlag, (1994).

[8] A.N. KOLMOGOROV & S.V.FOMIN, Introductory Real Analysis, Dover Publications, INC., New York, (1975).

[9] E. MONTENEGRO, R. SALAZAR, A result about the incidents edges in the graphs Mk, Discrete Mathematics, 122, pp. 277-280, (1993).

[10] E. MONTENEGRO, D. POWERS, S. RUIZ, R. SALAZAR, Spectra of related graphs and Self Reproducing Polyhedra, Proyecciones, 11, N o 1, pp. 01-09, (1992)

[11] E. MONTENEGRO, D. POWERS, S. RUIZ, R. SALAZAR, Automorphism Group and hamiltonian properties preserved by Substitution, Scientia, Serie A Math. Sciences 4, pp. 57-67, (1993).

[12] E. PRISNER, Graph Dynamics, version 2B, Universität Hamburg, Hamburg, F.R. Germany, (1994).

[13] R. ROCKAFELLAR, Convex Analysis, Princeton University Press, (1970).

Published

2017-04-24

How to Cite

[1]
E. Montenegro and E. Cabrera, “Attractors points in the autosubstitution”, Proyecciones (Antofagasta, On line), vol. 20, no. 2, pp. 193-204, Apr. 2017.

Issue

Section

Artículos