## Abstract

Let G be a connected graph of order p and S a nonempty set of vertices of G. Then the Steiner distance d(S) of S is the minimum size of a connected subgraph of G whose vertex set contains S. If n is an integer, 2≤n≤p, the Steiner n-diameter, diam_{n}(G), of G is the maximum Steiner distance of any n-subset of vertices of G. This is a generalisation of the ordinary diameter, which is the case n=2. We give upper bounds on the Steiner n-diameter of maximum planar graphs in terms of order and connectivity. Moreover, we construct graphs to show that the bound is asymptotically sharp. Furthermore we extend this result to 4 and 5-connected maximal planar graphs.

Original language | English |
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Pages (from-to) | 222-228 |

Number of pages | 7 |

Journal | Discrete Applied Mathematics |

Volume | 179 |

DOIs | |

Publication status | Published - 31 Dec 2014 |

## Keywords

- Diameter
- Distance
- Planar
- Steiner diameter
- Steiner distance

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics