Distance-residual subgraphs

For a connected finite graph GG and a subset V0V0 of its vertex set, a distance-residual subgraph is a subgraph induced on the set of vertices at the maximal distance from V0V0. Some properties and examples of distance-residual subgraphs of vertex-transitive, edge-transitive, bipartite and semisymmetric graphs are presented. The relations between the distance-residual subgraphs of product graphs and their factors are explored.