Wiener Indices of Maximal k-Degenerate Graphs

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.

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Work Title Wiener Indices of Maximal k-Degenerate Graphs
Open Access
  1. Allan Bickle
  2. Zhongyuan Che
License In Copyright (Rights Reserved)
Work Type Article
  1. Springer Science and Business Media LLC
Publication Date January 9, 2021
Publisher Identifier (DOI)
  1. 10.1007/s00373-020-02264-8
  1. Graphs and Combinatorics
Deposited May 27, 2022




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Work History

Version 1

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  • Added WI-k-Degenerate-10-25-20-1.pdf
  • Added Creator Allan Bickle
  • Added Creator Zhongyuan Che
  • Published
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