## Services on Demand

## Journal

## Article

## Indicators

## Related links

- Cited by Google
- Similars in SciELO
- Similars in Google

## Share

## Proyecciones (Antofagasta)

*Print version* ISSN 0716-0917

#### Abstract

MONTENEGRO, Eduardo et al. **GRAPHS r-POLAR SPHERICAL REALIZATIONP**.* Proyecciones (Antofagasta)* [online]. 2010, vol.29, n.1, pp.31-39.
ISSN 0716-0917. http://dx.doi.org/10.4067/S0716-09172010000100004.

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 P_{r} = (0, 0, 0, r) ? R^{4}, r ? R^{+} . The r-polar sphere, denoted by S_{Pr} , is defined by {x ? R^{4}/ ||x|| = 1 ? x ? P_{r} }: 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) ? S_{Pr} 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), P_{r} and the r-polar sphere.

**Keywords
:
**Graph; Sphere.