• DocumentCode
    1898456
  • 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
  • fYear
    2009
  • fDate
    15-19 Dec. 2009
  • Firstpage
    1
  • Lastpage
    3
  • 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;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Wireless Communication and Sensor Networks (WCSN), 2009 Fifth IEEE Conference on
  • Conference_Location
    Allahabad
  • Print_ISBN
    978-1-4244-5876-9
  • Type

    conf

  • DOI
    10.1109/WCSN.2009.5434812
  • Filename
    5434812
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1898456