Graphs r-polar spherical realization.
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Montenegro, Eduardo [1] ; Cabrera, Eduardo [1] ; González, José [1] ; Nettle, Alejandro [1] ; Robres, Ramón [1]
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[1] Universidad de Playa Ancha de Ciencias de la Educación
Universidad de Playa Ancha de Ciencias de la Educación
Valparaíso, Chile
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- Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 29, Nº. 1, 2010, págs. 31-39
- Idioma: inglés
- Enlaces
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Resumen
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.
