Antimagic orientations of graphs with given independence number

Given a digraph D with m arcs and a bijection tau : A(D) -> {1, 2, ... , m}, we say (D, tau) is an antimagic orientation of a graph G if D is an orientation of G and no two vertices in D have the same vertex-sum under tau, where the vertex-sum of a vertex u in D under tau is the sum of labels of all arcs entering u minus the sum of labels of all arcs leaving u. Hefetz, Mutze, and Schwartz in 2010 initiated the study of antimagic orientations of graphs, and conjectured that every connected graph admits an antimagic orientation. This conjecture seems hard, and few related results are known. However, it has been verified to be true for regular graphs, biregular bipartite graphs, and graphs with large maximum degree. In this paper, we establish more evidence for the aforementioned conjecture by studying antimagic orientations of graphs G with independence number at least vertical bar V(G)vertical bar/2 or at most four. We obtain several results. The method we develop in this paper may shed some light on attacking the aforementioned conjecture. (C) 2020 Elsevier B.V. All rights reserved.