Super Edge - Magic Strength of Fire Crackers, Banana Trees and Unicyclic Graphs

A graph G(V, E) is called super edge-magic if there exists a bijection f from V∪E, to {1,2,3,…, ∣F∣ + ∣-E∣} such that f(u)+f(v)+f(uv) = c(f) is constant for any uv ∈ E and f(V) =, {1, 2, 3,…, ∣V∣}., Such bijection is called a super edge-magic labeling of G. The super edge-magic strength of a graph G is denned as the minimum of all c(f) where the minimum runs over all super edge-magic labelings of G and is denoted by sm(G).