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The Size of Maximally Irregular Graphs and Maximally Irregular Triangle-Free Graphs

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Abstract

Let G be a graph. The irregularity index of G, denoted by t(G), is the number of distinct values in the degree sequence of G. For any graph G, t(G) ≤ Δ(G), where Δ(G) is the maximum degree. If t(G) = Δ(G), then G is called maximally irregular. In this paper, we give a tight upper bound on the size of maximally irregular graphs, and prove the conjecture proposed in [6] on the size of maximally irregular triangle-free graphs. Extremal graphs are also characterized.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, Xinjiang, People’s Republic of China

    Fengxia Liu, Zhao Zhang & Jixiang Meng

Authors
  1. Fengxia Liu
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  2. Zhao Zhang
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  3. Jixiang Meng
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Corresponding author

Correspondence to Zhao Zhang.

Additional information

This research is supported by NSFC (61222201,11171283) and SRFDP (20126501110001).

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Liu, F., Zhang, Z. & Meng, J. The Size of Maximally Irregular Graphs and Maximally Irregular Triangle-Free Graphs. Graphs and Combinatorics 30, 699–705 (2014). https://doi.org/10.1007/s00373-013-1304-1

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  • DOI: https://doi.org/10.1007/s00373-013-1304-1

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