## Print version ISSN 0716-0917

### Proyecciones (Antofagasta) vol.29 no.1 Antofagasta May 2010

#### http://dx.doi.org/10.4067/S0716-09172010000100004

Proyecciones Journal of Mathematics
Vol. 29, N° 1, pp. 31-39, May 2010.
Antofagasta - Chile

GRAPHS r-POLAR SPHERICAL REALIZATION*

Eduardo Montenegro
Eduardo Cabrera
José González
Alejandro Nettle
Ramón Robres

Correspondencia a:

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 Λ 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.

Keywords : Graph, Sphere.

AMS Subject Classifications : 05C25 ; 05C35.

References

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Received : October 2009. Accepted : January 2010

Eduardo Montenegro
Departamento de Matemáticas y Física
Facultad de Ciencias Naturales y Exactas
Casilla 34 V
Valparaíso
e-mail : emontene@upla.cl

Eduardo Cabrera
Departamento de Matemáticas y Física
Facultad de Ciencias Naturales y Exactas
Casilla 34 V
Valparaíso
e-mail : ecabrera@upla.cl

José González
Departamento de Matemáticas y Física
Facultad de Ciencias Naturales y Exactas
Casilla 34 V
Valparaíso
e-mail : egonzalez@upla.cl

Alejandro Nettle
Departamento de Matemáticas y Física
Facultad de Ciencias Naturales y Exactas
Casilla 34 V
Valparaíso
e-mail : anettle@upla.cl

Ramón Robres
Departamento de Matemáticas y Física
Facultad de Ciencias Naturales y Exactas