On graceful antimagic graphs

A graceful labeling of a graph G is an injective function from the vertex set of G to the set { 0 , 1 , ⋯ , | E ( G ) | } such that the induced edge labels are all different, where an induced edge label is defined as the absolute value of the difference between the labels of its end vertices. If the induced edge labeling is simultaneously antimagic, i.e., the sums of labels of all edges incident to a given vertex are pairwise distinct for different vertices, we say that the graceful labeling is graceful antimagic. In this paper we deal with the problem of finding some classes of graceful antimagic graphs.