The hull number of an oriented graph
نویسندگان
چکیده
منابع مشابه
The Hull Number of an Oriented Graph
We present characterizations of connected graphs G of order n ≥ 2 for which h + (G) = n. It is shown that for every two integers n and m with 1 ≤ n − 1 ≤ m ≤ n 2 , there exists a connected graph G of order n and size m such that for each integer k with 2 ≤ k ≤ n, there exists an orientation of G with hull number k. 1. Introduction. The (directed) distance d(u, v) from a vertex u to a vertex v i...
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متن کاملOn the hull number of some graph classes . 1
Given a graph G = (V, E), the closed interval of a pair of vertices u, v ∈ V , denoted by I[u, v], is the set of vertices that belongs to some shortest (u, v)-path. The convex hull I h [S] of a subset S ⊆ V is the smallest convex set that contains S. We say that S is a hull set if I h [S] = V. The cardinality of a minimum hull set of G is the hull number of G, denoted by hn(G). We show that dec...
متن کاملThe vertex detour hull number of a graph
For vertices x and y in a connected graph G, the detour distance D(x, y) is the length of a longest x− y path in G. An x− y path of length D(x, y) is an x − y detour. The closed detour interval ID[x, y] consists of x, y, and all vertices lying on some x − y detour of G; while for S ⊆ V (G), ID[S] = ⋃ x,y∈S ID[x, y]. A set S of vertices is a detour convex set if ID[S] = S. The detour convex hull...
متن کاملOn the hull number of some graph classes
Given a graph G = (V,E), the closed interval of a pair of vertices u, v ∈ V , denoted by I[u, v], is the set of vertices that belongs to some shortest (u, v)-path. For a given S ⊆ V , let I[S] = ⋃ u,v∈S I[u, v]. We say that S ⊆ V is a convex set if I[S] = S. The convex hull Ih[S] of a subset S ⊆ V is the smallest convex set that contains S. We say that S is a hull set if Ih[S] = V . The cardina...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2003
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171203210577