# Publications and Preprints

Size of the Giant Component in a Random Geometric Graph
by
Ghurumuruhan Ganesan
In this paper, we study the size of the giant component $C_G$ in the random geometric graph $G = G(n,r_n, f)$ of $n$ nodes independently distributed each according to a certain density $f(.)$ in $[0,1]^2$ satisfying $\inf_{x \in [0,1]^2} f(x)~>$~$0.$ If $\frac{c_1}{n} \leq r_n^2 \leq c_2\frac{\log{n}}{n}$ for some positive constants $c_1, c_2$ and $nr_n^2 \longrightarrow \infty,$ we show that %for some positive numbers $\epsilon_1$ sufficiently large and $\epsilon_2,$ the giant component of $G$ contains at least $n - o(n)$ nodes with probability at least $1 - o(1)$ as $n \rightarrow \infty.$ We also obtain estimates on the diameter and number of the non-giant components of $G.$

isid/ms/2012/13 [fulltext]