A method to generate large classes of edge-antimagic trees

Abstract

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.