Regular Graphs are Antimagic

Kristóf Bérczi, Attila Bernáth, Máté Vizer


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 $k\ge 2$.


Graph theory; Antimagic labeling; Regular graphs

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