منابع مشابه
The forcing geodetic number of a graph
For two vertices u and v of a graph G, the set I(u, v) consists of all vertices lying on some u − v geodesic in G. If S is a set of vertices of G, then I(S) is the union of all sets I(u, v) for u, v ∈ S. A set S is a geodetic set if I(S) = V (G). A minimum geodetic set is a geodetic set of minimum cardinality and this cardinality is the geodetic number g(G). A subset T of a minimum geodetic set...
متن کاملThe Upper Edge Geodetic Number and the Forcing Edge Geodetic Number of a Graph
An edge geodetic set of a connected graph G of order p ≥ 2 is a set S ⊆ V (G) such that every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g1(G) of G is the minimum cardinality of its edge geodetic sets and any edge geodetic set of cardinality g1(G) is a minimum edge geodetic set of G or an edge geodetic basis of G. An edge geodetic set S in ...
متن کاملDouble geodetic number of a graph
For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v ∈ S such that x, y ∈ I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic of cardinality dg(G) is called dg-set of G. The double geodetic numbers of certain standard graphs are o...
متن کاملThe 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...
متن کاملThe Restrained Edge Geodetic Number of a Graph
A set S of vertices of a connected graph G is a geodetic set if every vertex of G lies on an x−y geodesic for some elements x and y in S. The minimum cardinality of a geodetic set ofG is the geodetic number ofG, denoted by g(G). A set S of vertices of a graph G is an edge geodetic set if every edge of G lies on an x − y geodesic for some elements x and y in S. The minimum cardinality of an edge...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2000
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0301