  Given a graph $G$ and a positive integer $R$ we address the following
combinatorial search theoretic problem: What is the minimum number of queries
of the form "does an unknown vertex $v \in V(G)$ belong to the ball of radius
$r$ around $u$?" with $u \in V(G)$ and $r\le R$ that is needed to determine
$v$. We consider both the adaptive case when the $j$th query might depend on
the answers to the previous queries and the non-adaptive case when all queries
must be made at once. We obtain bounds on the minimum number of queries for
hypercubes, the Erd\H os-R\'enyi random graphs and graphs of bounded maximum
degree .
