Enumerating super edge-magic labelings for the union of nonisomorphic graphs

Abstract

A super edge-magic labeling of a graph G=(V,E) of order p and size q is a bijection f:V U E → {i}p+qi=1 such that: (1) f(u)+f(uv)+f(v)=k for all uv ε E; and (2) f(V )={i}pi=1. Furthermore, when G is a linear forest, the super edge-magic labeling of G is called strong if it has the extra property that if uv ε E(G) , u',v' ε V (G) and dG (u,u' )=dG (v,v' )