<p>This paper addresses the stability issue of discrete-time linear systems with multiple constrained delays described by a certain delay digraph. Employing the information of delays and system matrices, a switch digraph is constructed and, compared to the delay digraph, has possibly less vertices and edges. By means of the switch digraph, a switch transform method is utilized to transform the original system into an equivalent switched system. By employing the switched homogeneous Lyapunov function (SHLF) approach, a necessary and sufficient exponential stability condition is established. All the presented results can be applied to the general situations (non-constrained delays) without any modification.</p>