Anti-magic labeling of regular graphs
A graph $G=(V,E)$ is antimagic if there is a one-to-one correspondence $f: E \to \{1,2,\ldots, |E|\}$ such that for any two vertices $u,v$, $\sum_{e \in E(u)}f(e) \ne \sum_{e\in E(v)}f(e)$. It is known that bipartite regular graphs are antimagic and non-bipartite regular graphs of odd degree at leas...
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| Zusammenfassung: | A graph $G=(V,E)$ is antimagic if there is a one-to-one correspondence $f: E
\to \{1,2,\ldots, |E|\}$ such that for any two vertices $u,v$, $\sum_{e \in
E(u)}f(e) \ne \sum_{e\in E(v)}f(e)$. It is known that bipartite regular graphs
are antimagic and non-bipartite regular graphs of odd degree at least three are
antimagic. Whether all non-bipartite regular graphs of even degree are
antimagic remained an open problem. In this paper, we solve this problem and
prove that all even degree regular graphs are antimagic. The paper was
submitted to December 2014 by Journal of Graph Theory. |
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| DOI: | 10.48550/arxiv.1505.07688 |