The Antimagic Orientations for Graphs Obtained by Some Graph Operations

A simple graph G is said to admit an antimagic orientation if there exist such that the vertex sums of vertices are pairwise distinct, where the vertex sum of a vertex is defined to be the sum of the labels of the in-edges minus that of the out-edges incident to the vertex. It was conjectured by Hefetz, Mu<spacing diaeresis>tze, and Schwartz [9] in 2010 that every connected simple graph admits an antimagic orientation. In this paper, we prove that several operations on graphs such as the corona product, the lexicographic product, and the Mycielski construction, together with some conditions on the graphs yield graphs satisfying the above conjecture.