Number of Edges in Random Intersection Graph on Surface of a Sphere
| dc.creator | gupta, Bhupendra | |
| dc.date | 2008-09-06 | |
| dc.date.accessioned | 2026-07-07T10:01:16Z | |
| dc.date.available | 2026-07-07T10:01:16Z | |
| dc.description | In this article, we consider `$N$'spherical caps of area $4πp$ were uniformly distributed over the surface of a unit sphere. We study the random intersection graph $G_N$ constructed by these caps. We prove that for $p = \frac{c}{N^{\al}},\:c >0$ and $\al >2,$ the number of edges in graph $G_N$ follow the Poisson distribution. Also we derive the strong law results for the number of isolated vertices in $G_N$: for $p = \frac{c}{N^{\al}},\:c >0$ for $\al < 1,$ there is no isolated vertex in $G_N$ almost surely i.e., there are atleast $N/2$ edges in $G_N$ and for $\al >3,$ every vertex in $G_N$ is isolated i.e., there is no edge in edge set $\cE_N.$ | |
| dc.identifier | https://arxiv.org/abs/0809.1143 | |
| dc.identifier | http://arxiv.org/abs/0809.1143 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168577 | |
| dc.subject | Probability | |
| dc.title | Number of Edges in Random Intersection Graph on Surface of a Sphere | |
| dc.type | text |