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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 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.

Keywords : Graph; Sphere.

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