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Wiener Indices of Maximal k-Degenerate Graphs

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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 \(n \ge k \ge 1\). A graph is chordal if every induced cycle in the graph is a triangle and chordal maximal k-degenerate graphs of order \(n \ge k\) are k-trees. For k-trees of order \(n \ge 2k+2\), we characterize all extremal graphs for the upper bound.

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Acknowledgements

The authors would like to thank the referees for their helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Penn State University, Altoona Campus, Altoona, PA, 16601, USA

    Allan Bickle

  2. Department of Mathematics, Penn State University, Beaver Campus, Monaca, PA, 15061, USA

    Zhongyuan Che

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  1. Allan Bickle
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  2. Zhongyuan Che
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Correspondence to Zhongyuan Che.

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Bickle, A., Che, Z. Wiener Indices of Maximal k-Degenerate Graphs. Graphs and Combinatorics 37, 581–589 (2021). https://doi.org/10.1007/s00373-020-02264-8

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  • DOI: https://doi.org/10.1007/s00373-020-02264-8

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