  If we are given a connected finite graph $G$ and a subset of its vertices
$V_{0}$, we define a distance-residual graph as a graph induced on the set of
vertices that have the maximal distance from $V_{0}$. Some properties and
examples of distance-residual graphs of vertex-transitive, edge-transitive,
bipartite and semisymmetric graphs are shown. The relations between the
distance-residual graphs of product graphs and their factors are shown.
