A method to generate large classes of edge-antimagic trees

A (p, q)-graph G is said to be graceful if the vertices can be assigned the labels {1, 2, ... , q + 1} such that the absolute value of the difference in vertex labels between adjacent vertices generate the set {1, 2, ... , q} An (a, d)-edge-antimagic total labeling on a (p, q)-graph is defined as a one-to-one map taking the vertices and the edges onto the integers 1, 2,...,p + q with the property that the edge-weights (sums of endpoint labels and the edge label) form an arithmetic sequence starting from a and having a common difference d. In this paper we use the connection between graceful labelings and edge-antimagic labelings for generating large classes of edge-antimagic total trees from smaller graceful trees.