GRAPHS r-POLAR SPHERICAL REALIZATIONP
| Autor: | Alejandro Nettle, Edersson Cabrera, Ramón Robres, Eduardo Montenegro, José González |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Proyecciones (Antofagasta) v.29 n.1 2010 SciELO Chile CONICYT Chile instacron:CONICYT Proyecciones (Antofagasta), Volume: 29, Issue: 1, Pages: 31-39, Published: MAY 2010 |
| ISSN: | 0716-0917 |
| DOI: | 10.4067/s0716-09172010000100004 |
| Popis: | 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 S Pr , 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) ? 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), Pr and the r-polar sphere. |
| Databáze: | OpenAIRE |
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