Irregularity of Graphs Respecting Degree Bounds

Pub Date : 2023-11-03 DOI:10.37236/11948

Dieter Rautenbach, Florian Werner

引用次数: 0

Abstract

Albertson defined the irregularity of a graph $G$ as $$irr(G)=\sum\limits_{uv\in E(G)}|d_G(u)-d_G(v)|.$$ For a graph $G$ with $n$ vertices, $m$ edges, maximum degree $\Delta$, and $d=\left\lfloor \frac{\Delta m}{\Delta n-m}\right\rfloor$, we show $$irr(G)\leq d(d+1)n+\frac{1}{\Delta}\left(\Delta^2-(2d+1)\Delta-d^2-d\right)m.$$

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关于度界的图的不规则性

Albertson将图形$G$的不规则性定义为$$irr(G)=\sum\limits_{uv\in E(G)}|d_G(u)-d_G(v)|.$$对于具有$n$顶点、$m$边、最大度数$\Delta$和$d=\left\lfloor \frac{\Delta m}{\Delta n-m}\right\rfloor$的图形$G$，我们显示 $$irr(G)\leq d(d+1)n+\frac{1}{\Delta}\left(\Delta^2-(2d+1)\Delta-d^2-d\right)m.$$

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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