Super edge-magic strength of fire crackers, banana trees and unicyclic graphs

A graph G(V,E)G(V,E) is called super edge-magic if there exists a bijection f   from V∪EV∪E to {1,2,3,…,|V|+|E|}{1,2,3,…,|V|+|E|} such that f(u)+f(v)+f(uv)=c(f)f(u)+f(v)+f(uv)=c(f) is constant for any uv∈Euv∈E and f(V)={1,2,3,…,|V|}f(V)={1,2,3,…,|V|}. Such a bijection is called a super edge-magic labeling of G. The super edge-magic strength of a graph G   is defined as the minimum of all c(f)c(f) where the minimum runs over all super edge-magic labelings of G   and is denoted by sm(G)sm(G). The super edge-magic strength of some families of graphs are obtained in this paper.