Czechoslovak Mathematical Journal, Vol. 72, No. 3, pp. 735-746, 2022


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

Xiaoqian Liu, Xiaodan Chen, Junli Hu, Qiuyun Zhu

Received April 5, 2021.   Published online April 20, 2022.

Abstract:  The irregularity of a graph $G=(V, E)$ is defined as the sum of imbalances $|d_u-d_v|$ over all edges $uv\in E$, where $d_u$ 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 ($1\leq p \leq n-1$), and characterize the corresponding extremal graphs.
Keywords:  graph irregularity; connected graph; pendant vertex; extremal graph
Classification MSC:  05C07, 05C35


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Affiliations:   Xiaoqian Liu, Xiaodan Chen (corresponding author), Junli Hu, Qiuyun Zhu, College of Mathematics and Information Science, Guangxi University, No. 100, Daxue Road, Nanning, Guangxi, P. R. China, e-mail: xqliu95@163.com, x.d.chen@live.cn, hujunli3020@163.com, zhuqiuyun970302@163.com


 
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