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For two vertices u and v in a graph G = (V, E), the detour distance D(u, v) is the length of a longest u–v path in G. A u–v path of length D(u, v) is called a u–v detour. A set S ⊆ V is called an edge detour set if every edge in G lies on a detour joining a pair of vertices of S. The edge detour number dn 1 (G) of G is the minimum order of its edge detour… (More)

For two vertices u and v in a graph G = (V, E), the distance d(u, v) and detour distance D(u, v) are the length of a shortest or longest u − v path in G, respectively, and the Smarandache distance d i S (u, v) is the length d(u, v) + i(u, v) of a u − v path in G, where 0 ≤ i(u, v) ≤ D(u, v) − d(u, v). A u − v path of length d i S (u, v), if it exists, is… (More)

- DETOUR GRAPH, A. P. SANTHAKUMARAN, S. ATHISAYANATHAN, A. P. Santhakumaran, S. Athisayanathan
- 2010

For two vertices u and v in a graph G = (V, E), the detour distance D(u, v) is the length of a longest u–v path in G. A u–v path of length D(u, v) is called a u–v detour. A set S ⊆ V is called an edge detour set if every edge in G lies on a detour joining a pair of vertices of S. The edge detour number dn1(G) of G is the minimum order of its edge detour… (More)

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