GRAPHS r-POLAR SPHERICAL REALIZATIONP

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: Montenegro,Eduardo, Cabrera,Eduardo, González,José, Nettle,Alejandro, Robres,Ramón
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2010
Materias:
Graph
Sphere
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000100004
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spelling oai:scielo:S0716-091720100001000042010-05-19GRAPHS r-POLAR SPHERICAL REALIZATIONPMontenegro,EduardoCabrera,EduardoGonzález,JoséNettle,AlejandroRobres,Ramón Graph Sphere 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.29 n.1 20102010-05-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000100004en10.4067/S0716-09172010000100004
institution Scielo Chile
collection Scielo Chile
language English
topic Graph
Sphere
spellingShingle Graph
Sphere
Montenegro,Eduardo
Cabrera,Eduardo
González,José
Nettle,Alejandro
Robres,Ramón
GRAPHS r-POLAR SPHERICAL REALIZATIONP
description 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.
author Montenegro,Eduardo
Cabrera,Eduardo
González,José
Nettle,Alejandro
Robres,Ramón
author_facet Montenegro,Eduardo
Cabrera,Eduardo
González,José
Nettle,Alejandro
Robres,Ramón
author_sort Montenegro,Eduardo
title GRAPHS r-POLAR SPHERICAL REALIZATIONP
title_short GRAPHS r-POLAR SPHERICAL REALIZATIONP
title_full GRAPHS r-POLAR SPHERICAL REALIZATIONP
title_fullStr GRAPHS r-POLAR SPHERICAL REALIZATIONP
title_full_unstemmed GRAPHS r-POLAR SPHERICAL REALIZATIONP
title_sort graphs r-polar spherical realizationp
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2010
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000100004
work_keys_str_mv AT montenegroeduardo graphsrpolarsphericalrealizationp
AT cabreraeduardo graphsrpolarsphericalrealizationp
AT gonzalezjose graphsrpolarsphericalrealizationp
AT nettlealejandro graphsrpolarsphericalrealizationp
AT robresramon graphsrpolarsphericalrealizationp
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