Geodesic
The extremal irregularity of connected graphs with given number of pendant vertices
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 735-746.

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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.
DOI : 10.21136/CMJ.2022.0125-21
Classification : 05C07, 05C35
Keywords: graph irregularity; connected graph; pendant vertex; extremal graph 
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Liu, Xiaoqian; Chen, Xiaodan; Hu, Junli; Zhu, Qiuyun. The extremal irregularity of connected graphs with given number of pendant vertices. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 735-746. doi : 10.21136/CMJ.2022.0125-21. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0125-21/

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