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- S. Athisayanathan, A. P. Santhakumaran
- Discussiones Mathematicae Graph Theory
- 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)

- I. Keerthi Asir, S. Athisayanathan
- Discrete Math., Alg. and Appl.
- 2017

In this paper, we define the clique-to-vertex C–v monophonic path, the clique-to-vertex monophonic distance dm(C, v), the clique-to-vertex monophonic eccentricity em2(C), the clique-to-vertex monophonic radius Rm2 , and the clique-to-vertex monophonic diameter Dm2 , where C is a clique and v a vertex in a connected graph G. We determine these parameters for… (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)

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 diS(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 diS(u, v), if it exists, is called a… (More)

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. For subsets A and B of V, the detour distance D (A, B) is defined as D (A, B) = min {D (x, y) : x ∈ A, y ∈ B}. A u – v path of length D (A, B) is called an A – B detour joining the… (More)

- A. P. Santhakumaran, S. Athisayanathan
- Ars Comb.
- 2011

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