Antimagic orientations of graphs with given independence number

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