The edge-Wiener index of a graph

P. Dankelmann, I. Gutman, S. Mukwembi, H. C. Swart

Research output: Contribution to journalArticlepeer-review

98 Citations (Scopus)

Abstract

If G is a connected graph, then the distance between two edges is, by definition, the distance between the corresponding vertices of the line graph of G. The edge-Wiener index We of G is then equal to the sum of distances between all pairs of edges of G. We give bounds on We in terms of order and size. In particular we prove the asymptotically sharp upper bound We (G) ≤ frac(25, 55) n5 + O (n9 / 2) for graphs of order n.

Original languageEnglish
Pages (from-to)3452-3457
Number of pages6
JournalDiscrete Mathematics
Volume309
Issue number10
DOIs
Publication statusPublished - 28 May 2009
Externally publishedYes

Keywords

  • Distance
  • Line graph
  • Wiener index

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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