Super edge-magic total labeling of a tree

Abstract

An edge-magic total labeling of a graph G is a one-toone map λ from V(G) ∪ E(G) onto the integers {1, 2, ⋯, |V(G) ∪ E5(G)|} with the property that, there is an integer constant c such that λ(x) + λ(xy) + λ(y) = c for any xy ∈ E(G). If λ(V(G)) = {1, 2, ⋯, | V(G|} then edge-magic total labeling is called super edgemagic total labeling. In this paper we investigate super edge-magic total labeling on w-trees.