Title :
Strong law for number of edges on surface of a unit sphere
Author :
Gupta, Bhupendra ; Pandey, Arvind
Author_Institution :
Dept. of Comput. Sci. & Eng., Indian Inst. of Inf. Technol. (DM), Jabalpur, India
Abstract :
In this article, we consider `N´ spherical caps of area 4¿p were uniformly distributed over the surface of a unit sphere. We study the random intersection graph GN constructed by these caps. we derive the strong law results for the number of isolated vertices in GN: for p = c/Nr, c > 0 for r < 1, there is no isolated vertex in GN almost surely i.e., there are atleast N/2 edges in GN and for r > 3, every vertex in GN is isolated i.e., there is no edge in edge set ¿N.
Keywords :
graph theory; wireless sensor networks; N spherical caps; isolated vertex; isolated vertices; number of edges on surface; random intersection graph; unit sphere; Bipartite graph; Computer science; Information technology; Local area networks; Portable computers; Radio propagation; Statistical distributions; Wireless LAN; Wireless sensor networks;
Conference_Titel :
Wireless Communication and Sensor Networks (WCSN), 2009 Fifth IEEE Conference on
Conference_Location :
Allahabad
Print_ISBN :
978-1-4244-5876-9
DOI :
10.1109/WCSN.2009.5434812
