An undirected simple graph $G=(V,E)$ is called antimagic if there exists an injective function $f:E\rightarrow\{1,\dots,|E|\}$ such that $\sum_{e\in E(u)} f(e)\neq\sum_{e\in E(v)} f(e)$ for any pair of different nodes $u,v\in V$. In this note we prove — with a slight modification of an argument of Cranston et al. — that $k$-regular graphs are antimagic for $k\ge 2$. A corrigendum was added to this paper on May 2, 2019.
@article{10_37236_5465,
author = {Krist\'of B\'erczi and Attila Bern\'ath and M\'at\'e Vizer},
title = {Regular graphs are antimagic},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {3},
doi = {10.37236/5465},
zbl = {1323.05110},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5465/}
}
TY - JOUR
AU - Kristóf Bérczi
AU - Attila Bernáth
AU - Máté Vizer
TI - Regular graphs are antimagic
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/5465/
DO - 10.37236/5465
ID - 10_37236_5465
ER -
%0 Journal Article
%A Kristóf Bérczi
%A Attila Bernáth
%A Máté Vizer
%T Regular graphs are antimagic
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/5465/
%R 10.37236/5465
%F 10_37236_5465
Kristóf Bérczi; Attila Bernáth; Máté Vizer. Regular graphs are antimagic. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/5465
