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The paper introduces a graph theory variation of the general position problem: given a graph 
$G$, determine a largest set 
$S$ of vertices of 
$G$ such that no three vertices of 
$S$ lie on a common geodesic. Such a set is a max-gp-set of 
$G$ and its size is the gp-number 
$\text{gp}(G)$ of 
$G$. Upper bounds on 
$\text{gp}(G)$ in terms of different isometric covers are given and used to determine the gp-number of several classes of graphs. Connections between general position sets and packings are investigated and used to give lower bounds on the gp-number. It is also proved that the general position problem is NP-complete.
