## Abstract

Let G be a connected graph. The Steiner distance d(S) of a set S of vertices is the minimum size of a connected subgraph of G containing all vertices of S. For k∈N, the Steiner k-Wiener index SW_{k}(G) is defined as ∑_{S}d(S), where the sum is over all k-element subsets of the vertex set of G. The average Steiner k-distance μ_{k}(G) of G is defined as [Formula presented]. In this paper we prove upper bounds on the Steiner Wiener index and the average Steiner distance of graphs with given order n and minimum degree δ. Specifically we show that [Formula presented]. We improve this bound for triangle-free graphs to [Formula presented]. All bounds are best possible.

Original language | English |
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Pages (from-to) | 35-43 |

Number of pages | 9 |

Journal | Discrete Applied Mathematics |

Volume | 268 |

DOIs | |

Publication status | Published - 15 Sept 2019 |

## Keywords

- Average distance
- Average steiner distance
- Steiner Wiener index
- Steiner distance
- Transmission
- Wiener index

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics