Graphs r-polar spherical realization.
DOI:
https://doi.org/10.4067/S0716-09172010000100004Keywords:
Graph, sphere, grafos, esferas.Abstract
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.References
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Montenegro, E., Powers, D., Ruíz, S., Salazar, R. Spectra of related graphs and Self Reproducing Polyhedra, Proyecciones, v 11, pp. 01- 09, (1992).
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Published
2011-01-06
How to Cite
[1]
E. Montenegro, E. Cabrera, J. González, A. Nettle, and R. Robres, “Graphs r-polar spherical realization.”, Proyecciones (Antofagasta, On line), vol. 29, no. 1, pp. 31-39, Jan. 2011.
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