Abstract
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, Mütze, 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.
Highlights
Unless otherwise stated explicitly, all graphs considered are simple and finite
A labeling is antimagic if it is vertex distinguishable and S = {1, 2, · · ·, m}
A graph is antimagic if it has an antimagic labeling
Summary
All graphs considered are simple and finite. A labeling of a graph G with m edges is a bijection from E(G) to a set S of m integers, and the vertex sum at a vertex v ∈ V (G) is the sum of labels on the edges incident to v. By the assignment of labels on edges incident to yi with m + 1 ≤ i ≤ n, the sums at yi are pairwise distinct.
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