Title :
A very strong zero-one law for connectivity in one-dimensional geometric random graphs
Author :
Han, Guang ; Makowski, Armand M.
Author_Institution :
Dept. of Electr. & Comput. Eng., Maryland Univ., College Park, MD
Abstract :
We consider the geometric random graph where n points are distributed uniformly and independently on the unit interval [0, 1]. Using the method of first and second moments, we provide a simple proof of a very strong "zero-one" law for the property of graph connectivity under the asymptotic regime created by having n become large and the transmission range scaled appropriately with u
Keywords :
graph theory; radio networks; asymptotic regime; graph connectivity; one-dimensional geometric random graph; transmission range; wireless network; zero-one law; Displays; Helium; Solid modeling; Wireless networks;
Journal_Title :
Communications Letters, IEEE
DOI :
10.1109/LCOMM.2007.061142
