We know the diameter of a random graph with $n$ vertices is $log(n)$.
Consider a random graph $G_{(n,p)} = (V,E)$ and a vertex $v\in V$. We start a random walk from $v$. How long take this random walk traverse the diameter of $G$? In other words, there are many vertices ($U=\{u_{1},u_{2},...\})$ that their distance from $v$ are $log(n), \Big(\forall u \in U : dist(v,u) = O(log(n))\Big)$. How long take the random walk started from $v$ reaches to one of members in $U$?
- Does this problem have a name like hitting time or cover time?