On the k-Connectivity of Ad-Hoc Wireless Networks
Bhupendra Gupta, Ashish Gupta · 2013
In this paper, we consider k-connectivity problem which is one of the fundamental problems in the ad-hoc wireless network. Here we assume that the nodes are uniformly distributed on a unit square area [0, 1]2. We define a random graph on unit square [0, 1]2and derive the critical range for transmission radius rnto achieving k-connectivity of a randomly generated network in almost sure sense. We prove that if rnis defined as rn2:=1/nr(c log n + (k-1)log2n - logΓ(k)), where k, c>0 are constants and n be the number of node in the network, then for c>2 the network is a k-connected network in almost sure sense. Also we derive that for c>2 and critical transmission range Cn= √(clog n/nr) the network is connected.