Wiener Indices of Maximal k-Degenerate Graphs

Allan Bickle; Zhongyuan Che

doi:10.1007/s00373-020-02264-8

Wiener Indices of Maximal k-Degenerate Graphs

Allan Bickle
, Zhongyuan Che

Penn State Beaver

Research output: Contribution to journal › Article › peer-review

12 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 language	English (US)
Pages (from-to)	581-589
Number of pages	9
Journal	Graphs and Combinatorics
Volume	37
Issue number	2
DOIs	https://doi.org/10.1007/s00373-020-02264-8
State	Published - Mar 2021

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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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≥ 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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AB - 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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Wiener Indices of Maximal k-Degenerate Graphs

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