GRAPHS r-POLAR SPHERICAL REALIZATIONP
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 ? P...
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| Autores principales: | , , , , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2010
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000100004 |
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| Sumario: | 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. |
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