The Unit Acquisition Number of Binomial Random Graphs

Let $G$ be a graph in which each vertex initially has weight 1. In step, the unit from $u$ to neighbouring $v$ can moved, provided that on is at least as large $u$. The acquisition number of $G$, denoted by $a_u(G)$, minimum cardinality set vertices with positive end process (over all protocols). this paper, we investigate Erdős-Rényi random $(\mathcal{G}(n,m))_{m =0}^{N}$, where $N = {n \choose 2}$. We show asymptotically almost surely $a_u(\mathcal{G}(n,m)) 1$ right time step creates connected graph. Since trivially \ge 2$ if graphs disconnected, result holds strongest possible sense.