Diameter and inverse degree

Peter Dankelmann; Henda C. Swart; Paul van den Berg

doi:10.1016/j.disc.2007.07.053

Diameter and inverse degree

Peter Dankelmann, Henda C. Swart, Paul van den Berg

University of KwaZulu-Natal

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

30 Citations (Scopus)

Abstract

The inverse degree r (G) of a finite graph G = (V, E) is defined as r (G) = ∑_{v ∈ V} frac(1, deg v). We prove that, if G is connected and of order n, then the diameter of G is less than (3 r (G) + 2 + o (1)) frac(log n, log log n). This improves a bound given by Erdös et al. by a factor of approximately 2.

Original language	English
Pages (from-to)	670-673
Number of pages	4
Journal	Discrete Mathematics
Volume	308
Issue number	5-6
DOIs	https://doi.org/10.1016/j.disc.2007.07.053
Publication status	Published - 28 Mar 2008
Externally published	Yes

Keywords

Diameter
Distance
Inverse degree

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2007.07.053

Cite this

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Diameter and inverse degree

Abstract

Keywords

ASJC Scopus subject areas

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