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Antimagic orientation of biregular bipartite graphs. (arXiv:1706.07336v1 [math.CO])
来源于:arXiv
An antimagic labeling of a directed graph $D$ with $n$ vertices and $m$ arcs
is a bijection from the set of arcs of $D$ to the integers $\{1, \cdots, m\}$
such that all $n$ oriented vertex sums are pairwise distinct, where an oriented
vertex sum is the sum of labels of all arcs entering that vertex minus the sum
of labels of all arcs leaving it. An undirected graph $G$ is said to have an
antimagic orientation if $G$ has an orientation which admits an antimagic
labeling. Hefetz, M{\"{u}}tze, and Schwartz conjectured that every connected
undirected graph admits an antimagic orientation. In this paper, we support
this conjecture by proving that every biregular bipartite graph admits an
antimagic orientation. 查看全文>>