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

Xiaoqian LiuXiaodan ChenJunli HuQiuyun Zhu — 2022

Czechoslovak Mathematical Journal

The irregularity of a graph G = ( V , E ) is defined as the sum of imbalances | d u - d v | over all edges u v 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 p n - 1 ), and characterize the corresponding extremal graphs.

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