Abstract
An injective function f : V(G) -> {1, 2, ..., q + 1} is a graceful labeling of a (p, q)-graph G = (V, E) if when each edge uv is assigned the label vertical bar f(u) - f(v)vertical bar, the resulting edge labels (or weights) are distinct. An (a, d)-edge-antimagic vertex labeling on a (p, q)-graph is defined as a one-to-one map taking the vertices onto the integers 1, 2, ...,p with the property that the edge-weights (sums of endpoint labels) form an arithmetic sequence starting at a and having a common difference d.
In this paper we construct alpha-labeling (a special case of graceful labeling) of trees from graceful labelings of smaller trees and transform this labeling to edge-antimagic vertex labeling of trees.