On mean distance and girth

Authors:
Siham Bekkai;Mekkia Kouider
Affiliations:
LAID3, U.S.T.H.B, Faculté de Mathématiques, BP.32 El-Alia, Bab Ezzouar, 16111 Alger, Algérie;LRI, Université Paris-Sud, UMR 8623, Bít. 490,91405 Orsay Cedex, France
Venue:
Discrete Applied Mathematics
Year:
2010

Citing 6
Cited 0

Average distance and independence number

2nd Twente workshop on Graphs and combinatorial optimization
Mean distance and minimum degree

Journal of Graph Theory
Bounding the diameter and the mean distance of a graph from its eigenvalues: Laplacian versus adjacency matrix methods

Discrete Mathematics
Variable neighborhood search for extremal graphs: 1 the AutoGraphiX system

Discrete Mathematics
Using minimum degree to bound average distance

Discrete Mathematics
Average distance, minimum degree, and spanning trees

Journal of Graph Theory

Quantified Score

Hi-index	0.04

Visualization

Abstract

We bound the mean distance in a connected graph which is not a tree in terms of its order n and its girth g. On one hand, we show that the mean distance is at most n+13-g(g^2-4)12n(n-1)-g(g-2)(n-g)2n(n-1) if g is even and at most n+13-g(g^2-1)12n(n-1)-(g-1)^2(n-g)2n(n-1) if g is odd. On the other hand, we prove that the mean distance is at least ng4(n-1) unless G is an odd cycle. This resolves two conjectures of AutoGraphiX.