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 $$irr(G)\leq d(d+1)n+\frac{1}{\Delta}\left(\Delta^2-(2d+1)\Delta-d^2-d\right)m.$$
@article{10_37236_11948,
author = {Dieter Rautenbach and Florian Werner},
title = {Irregularity of graphs respecting degree bounds},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {4},
doi = {10.37236/11948},
zbl = {1532.05039},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11948/}
}
TY - JOUR
AU - Dieter Rautenbach
AU - Florian Werner
TI - Irregularity of graphs respecting degree bounds
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/11948/
DO - 10.37236/11948
ID - 10_37236_11948
ER -
%0 Journal Article
%A Dieter Rautenbach
%A Florian Werner
%T Irregularity of graphs respecting degree bounds
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/11948/
%R 10.37236/11948
%F 10_37236_11948
Dieter Rautenbach; Florian Werner. Irregularity of graphs respecting degree bounds. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/11948
