the order graphs of groups

let $g$ be a group. the order graph of $g$ is the (undirected)graph $gamma(g)$,those whose vertices are non-trivial subgroups of $g$ and two distinctvertices $h$ and $k$ are adjacent if and only if either$o(h)|o(k)$ or $o(k)|o(h)$. in this paper, we investigate theinterplay between the group-theoretic properties of $g$ and thegraph-theoretic properties of $gamma(g)$. for a finite group$g$, we show that $gamma(g)$ is a connected graph with diameter at mosttwo, and     $gamma(g)$ is a complete graph ifand only if $g$ is a $p$-group for some prime number $p$. furthermore,it is shown that $gamma(g)=k_5$ if and only if either$gcong c_{p^5}, c_3times c_3$, $c_2timesc_4$ or $gcong q_8$.