On the average Steiner distance of graphs with prescribed properties

Peter Dankelmann; Henda C. Swart; Ortrud R. Oellermann

doi:10.1016/S0166-218X(97)00035-8

On the average Steiner distance of graphs with prescribed properties

Peter Dankelmann, Henda C. Swart, Ortrud R. Oellermann

Research output: Contribution to journal › Article › peer-review

31 Citations (Scopus)

Abstract

The average n-distance of a connected graph G, μ_n(G), is the average of the Steiner distances of all n-sets of vertices of G. In this paper, we give bounds on μ_n for two-connected graphs and for k-chromatic graphs. Moreover, we show that μ_n(G) does not depend on the n-diameter of G.

Original language	English
Pages (from-to)	91-103
Number of pages	13
Journal	Discrete Applied Mathematics
Volume	79
Issue number	1-3
DOIs	https://doi.org/10.1016/S0166-218X(97)00035-8
Publication status	Published - 27 Nov 1997
Externally published	Yes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/S0166-218X(97)00035-8

Cite this

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title = "On the average Steiner distance of graphs with prescribed properties",

abstract = "The average n-distance of a connected graph G, μn(G), is the average of the Steiner distances of all n-sets of vertices of G. In this paper, we give bounds on μn for two-connected graphs and for k-chromatic graphs. Moreover, we show that μn(G) does not depend on the n-diameter of G.",

author = "Peter Dankelmann and Swart, \{Henda C.\} and Oellermann, \{Ortrud R.\}",

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AU - Dankelmann, Peter

AU - Swart, Henda C.

AU - Oellermann, Ortrud R.

PY - 1997/11/27

Y1 - 1997/11/27

N2 - The average n-distance of a connected graph G, μn(G), is the average of the Steiner distances of all n-sets of vertices of G. In this paper, we give bounds on μn for two-connected graphs and for k-chromatic graphs. Moreover, we show that μn(G) does not depend on the n-diameter of G.

AB - The average n-distance of a connected graph G, μn(G), is the average of the Steiner distances of all n-sets of vertices of G. In this paper, we give bounds on μn for two-connected graphs and for k-chromatic graphs. Moreover, we show that μn(G) does not depend on the n-diameter of G.

UR - https://www.scopus.com/pages/publications/0009086829

U2 - 10.1016/S0166-218X(97)00035-8

DO - 10.1016/S0166-218X(97)00035-8

M3 - Article

AN - SCOPUS:0009086829

SN - 0166-218X

VL - 79

SP - 91

EP - 103

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 1-3

ER -

On the average Steiner distance of graphs with prescribed properties

Abstract

ASJC Scopus subject areas

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