Wiener Indices of Maximal k-Degenerate Graphs

Allan Bickle, Zhongyuan Che

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A graph is maximal k-degenerate if each induced subgraph has a vertex of degree at most k and adding any new edge to the graph violates this condition. In this paper, we provide sharp lower and upper bounds on Wiener indices of maximal k-degenerate graphs of order n≥ k≥ 1. A graph is chordal if every induced cycle in the graph is a triangle and chordal maximal k-degenerate graphs of order n≥ k are k-trees. For k-trees of order n≥ 2 k+ 2 , we characterize all extremal graphs for the upper bound.

Original languageEnglish (US)
Pages (from-to)581-589
Number of pages9
JournalGraphs and Combinatorics
Volume37
Issue number2
DOIs
StatePublished - Mar 2021

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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