A Sequential Locating Game on Graphs

Abstract

Consider the game of locating a marked vertex on a connected graph,
where the player repeatedly chooses a vertex of the graph as a probe,
and is given the distance from the probe to the marked vertex,
until she can uniquely locate the hidden vertex. The goal is to
minimize the number of probes.

The static version of this game is the well-known problem of finding
the metric dimension (or location number ) of the graph.
We study the sequential version of this game, and the corresponding
sequential location number .