Graphs r-polar spherical realization.

  1. Montenegro, Eduardo 1
  2. Cabrera, Eduardo 1
  3. González, José 1
  4. Nettle, Alejandro 1
  5. Robres, Ramón 1
  1. 1 Universidad de Playa Ancha de Ciencias de la Educación
    info

    Universidad de Playa Ancha de Ciencias de la Educación

    Valparaíso, Chile

    ROR https://ror.org/0171wr661

Revista:
Proyecciones: Journal of Mathematics

ISSN: 0716-0917

Año de publicación: 2010

Volumen: 29

Número: 1

Páginas: 31-39

Tipo: Artículo

DOI: 10.4067/S0716-09172010000100004 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Proyecciones: Journal of Mathematics

Resumen

The graph to considered will be in general simple and finite, graphs with a nonempty set of edges. For a graph G, V(G) denote the set of vertices and E(G) denote the set of edges. Now, let Pr = (0, 0, 0, r) ? R4, r ? R+ . The r-polar sphere, denoted by SPr , is defined by {x ? R4/ ||x|| = 1 ? x ? Pr }: The primary target of this work is to present the concept of r-Polar Spherical Realization of a graph. That idea is the following one: If G is a graph and h : V (G) ? SPr is a injective function, them the r-Polar Spherical Realization of G, denoted by G*, it is a pair (V (G*), E(G*)) so that V (G*) = {h(v)/v ? V (G)} and E(G*) = {arc(h(u)h(v))/uv ? E(G)}, in where arc(h(u)h(v)) it is the arc of curve contained in the intersection of the plane defined by the points h(u), h(v), Pr and the r-polar sphere.

Referencias bibliográficas

  • Citas Barnsley, M. Fractal Everywhere, Academic Press, (1988).
  • Brondsted, A. An Introduction to Convex Polytopes, Springer Verlag, New York, Heidelberg, Berlin, (1983).
  • Chartrand G., Lesniaik, L. Graphs and Digraphs, Wadsworth and Brooks/Cole Advanced Books and Software Pacific Grove, C. A., (1996).
  • Chartrand G., Oellermann, O. Applied and Algorithmic Graph Theory, McGraw-Hill., Inc., (1993).
  • Coxeter, H. Regular Polytopes, Third Edition, Dover Publication, Inc, (1973).
  • Devaney, R. Introduction to Chaotic Dynamical Systems, 2nd edition, AddisonWesley, (1989).
  • Holmgren, R., A First Course in Discrete Dynamical Systems, Springer-Verlag, (1994).
  • Kolmogorov, A., Fomin, S.V. Introductory Real Analysis, Dover Publications, INC., New York, (1975).
  • Montenegro, E., Salazar R. A result about the incidents edges in the graphs Mk, Discrete Mathematics, 122, pp. 277-280, (1993).
  • Montenegro, E., Powers, D., Ruíz, S., Salazar, R. Spectra of related graphs and Self Reproducing Polyhedra, Proyecciones, v 11, pp. 01- 09, (1992).
  • Montenegro, E., Cabrera, E. Attractors Points in the Autosubstitution, Proyecciones, v 20, N 2, pp. 193-204, (2001).
  • Prisner, E. Graph Dynamics, version 213, Universitat Hamburg, Hamburg, F.R. Germany, (1994).
  • Rockafellar, R. Convex Analysis, Princeton University Press, (1970).
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