Super edge-magic strength of some trees

Abstract

A graph G is called super edge-magic if there exists a bijection f: V∪ E → {1,2,...,v + ε} such that for all edges xy. f(x) + f(y) + f(xy) = c(f) is a constant and f(V)= {1,2,...,v}.The super edge-magic strength of a graph is denoted by sm(G) and is defined as the minimum of all constants where the minimum is taken over all super edge-magic labelings of G. In this paper, we find the super edge-magic strength of some trees.