Distance-residual subgraphs

For a connected finite graph G and a subset V 0 of its vertex set, a distance-residual subgraph is a subgraph induced on the set of vertices at the maximal distance from V 0 . 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.