Detour Distance in Graphs

Abstract For vertices u and v in a connected graph G, the detour distance d* (u, v) between u and v is the length of a longest path P for which the subgraph induced by the vertices of P is P itself. A graph G is called a detour graph if d* (u, v) equals the standard distance between u and v in G for every pair u, v of vertices of G. Several results concerning detour distance and detour graphs are presented.