An all-path version of the Wiener index

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Abstract

The Wiener index W(G) has originally been defined for acyclic graphs. Therefore its extension to cycle-containing structures is not unambiguous; there are several possibilities, some of which have already been realized. In this paper, we proposed an "all-path" version of W and showed that its maximal value is equal to N2(N - 1)2N-4, where N denotes the number of vertices in a graph. In contrast, the maximal values of W and its close analogues, the detour index, w(G), and the Szeged index, Sz(G), are polynomials of order 4 or less in terms of N, and therefore, it may be expected that the new version will discriminate cycle-containing structures more efficiently than W(G), w(G), or Sz(G).

Original languageEnglish
Pages (from-to)125-129
Number of pages5
JournalJournal of Chemical Information and Computer Sciences
Volume38
Issue number2
Publication statusPublished - Mar 1998

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Polynomials
Values

ASJC Scopus subject areas

  • Chemistry(all)
  • Computational Theory and Mathematics
  • Computer Science Applications
  • Information Systems

Cite this

An all-path version of the Wiener index. / Lukovits, I.

In: Journal of Chemical Information and Computer Sciences, Vol. 38, No. 2, 03.1998, p. 125-129.

Research output: Contribution to journalArticle

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