Hub and global Hub numbers of a graph
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A set H of vertices in a graph G is a hub set of G, if for any u; v 2 V (G) n H, there is a uv-path with all intermediate vertices in H. A hub set H is a global hub set of G if it is a hub set of both G and its complement G: The minimum cardinality of a global hub set is called the global hub number hg(G) of G. In this paper we determine the global hub number of some standard graphs. Also upper and lower bounds for hg(G) are obtained. The relationship between hg(G) and other graph parameters is discussed.
Abstract
A set H of vertices in a graph G is a hub set of G, if for any u; v 2 V (G) n H, there is a uv-path with all intermediate vertices in H. A hub set H is a global hub set of G if it is a hub set of both G and its complement G: The minimum cardinality of a global hub set is called the global hub number hg(G) of G. In this paper we determine the global hub number of some standard graphs. Also upper and lower bounds for hg(G) are obtained. The relationship between hg(G) and other graph parameters is discussed.
참고문헌 (13)
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