Graphs r-polar spherical realization.

Authors

  • Eduardo Montenegro Universidad de Playa Ancha.
  • Eduardo Cabrera Universidad de Playa Ancha.
  • José González Universidad de Playa Ancha.
  • Alejandro Nettle Universidad de Playa Ancha.
  • Ramón Robres Universidad de Playa Ancha.

DOI:

https://doi.org/10.4067/S0716-09172010000100004

Keywords:

Graph, sphere, grafos, esferas.

Abstract

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.

Author Biographies

Eduardo Montenegro, Universidad de Playa Ancha.

Facultad de Ciencias Naturales y Exactas.
Departamento de Matemáticas y Física.

Eduardo Cabrera, Universidad de Playa Ancha.

Facultad de Ciencias Naturales y Exactas.
Departamento de Matemáticas y Física.

José González, Universidad de Playa Ancha.

Facultad de Ciencias Naturales y Exactas.
Departamento de Matemáticas y Física.

Alejandro Nettle, Universidad de Playa Ancha.

Facultad de Ciencias Naturales y Exactas.
Departamento de Matemáticas y Física.

Ramón Robres, Universidad de Playa Ancha.

Facultad de Ciencias Naturales y Exactas.
Departamento de Matemáticas y Física.

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Published

2011-01-06

How to Cite

[1]
E. Montenegro, E. Cabrera, J. González, A. Nettle, and R. Robres, “Graphs r-polar spherical realization.”, Proyecciones (Antofagasta, On line), vol. 29, no. 1, pp. 31-39, Jan. 2011.

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Section

Artículos