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The extremal irregularity of connected graphs with given number of pendant vertices

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Abstract

The irregularity of a graph G = (V, E) is defined as the sum of imbalances ∣du − dv∣ over all edges uv ∈ E, where du denotes the degree of the vertex u in G. This graph invariant, introduced by Albertson in 1997, is a measure of the defect of regularity of a graph. In this paper, we completely determine the extremal values of the irregularity of connected graphs with n vertices and p pendant vertices (1 ⩽ p ⩽ n − 1), and characterize the corresponding extremal graphs.

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Acknowledgements

The authors are very grateful to the anonymous referees for their valuable comments and suggestions, which have contributed to the final preparation of this paper.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, No. 100, Daxue Road, Nanning, Guangxi, P. R. China

    Xiaoqian Liu, Xiaodan Chen, Junli Hu & Qiuyun Zhu

Authors
  1. Xiaoqian Liu
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  2. Xiaodan Chen
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  3. Junli Hu
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  4. Qiuyun Zhu
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Corresponding author

Correspondence to Xiaodan Chen.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11861011) and by the special foundation for Guangxi Ba Gui Scholars.

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Liu, X., Chen, X., Hu, J. et al. The extremal irregularity of connected graphs with given number of pendant vertices. Czech Math J 72, 735–746 (2022). https://doi.org/10.21136/CMJ.2022.0125-21

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  • DOI: https://doi.org/10.21136/CMJ.2022.0125-21

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