Average distance, minimum degree, and size

Peter Dankelmann

Average distance, minimum degree, and size

Peter Dankelmann

University of KwaZulu-Natal

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

4 Citations (Scopus)

Abstract

We give an upper bound on the average distance of a. connected graph of given order, size, diameter, and minimum degree. As a corollary we show that the average distance of a connected graph of order n, size q and minimum degree δ ≥ 2 is at most ((n - √2q - ≥n)²(n + 2√2q - δn)) / ((δ + 1)n²)+O(1), for n, q large and δ constant. Our bound is shown to be best possible.

Original language	English
Pages (from-to)	233-243
Number of pages	11
Journal	Utilitas Mathematica
Volume	69
Publication status	Published - Mar 2006
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Cite this

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N2 - We give an upper bound on the average distance of a. connected graph of given order, size, diameter, and minimum degree. As a corollary we show that the average distance of a connected graph of order n, size q and minimum degree δ ≥ 2 is at most ((n - √2q - ≥n)2(n + 2√2q - δn)) / ((δ + 1)n2)+O(1), for n, q large and δ constant. Our bound is shown to be best possible.

AB - We give an upper bound on the average distance of a. connected graph of given order, size, diameter, and minimum degree. As a corollary we show that the average distance of a connected graph of order n, size q and minimum degree δ ≥ 2 is at most ((n - √2q - ≥n)2(n + 2√2q - δn)) / ((δ + 1)n2)+O(1), for n, q large and δ constant. Our bound is shown to be best possible.

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M3 - Article

AN - SCOPUS:33646532451

SN - 0315-3681

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EP - 243

JO - Utilitas Mathematica

JF - Utilitas Mathematica

ER -

Average distance, minimum degree, and size

Abstract

ASJC Scopus subject areas

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