# On the Steiner, geodetic and hull numbers of graphs

```@article{Hernando2005OnTS,
title={On the Steiner, geodetic and hull numbers of graphs},
author={M. Carmen Hernando and Tao Jiang and Merc{\`e} Mora and Ignacio M. Pelayo and Carlos Seara},
journal={Discrete Mathematics},
year={2005},
volume={293},
pages={139-154}
}```
Given a graph G and a subset W ⊆ V (G), a Steiner W -tree is a tree of minimum order that contains all of W . Let S(W ) denote the set of all vertices in G that lie on some Steiner W -tree; we call S(W ) the Steiner interval of W . If S(W ) = V (G), then we call W a Steiner set of G. The minimum order of a Steiner set of G is called the Steiner number of G. Given two vertices u, v in G, a shortest u − v path in G is called a u − v geodesic. Let I[u, v] denote the set of all vertices in G lying… CONTINUE READING

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