Solution to some open problems on E-super vertex magic labeling of disconnected graphs

摘要

An E-super vertex magic labeling is a bijection f :V(G)UE(G)→{1,2,3,…,p+q} such that for each vertex u, f(u)+∑v∈N(u)f(uv)=k for some constant k where f(E(G))={1,2,3,…,q}. A graph that admits an E-super vertex magic labeling is called an E-super vertex magic graph. The only disconnected graphs that have been shown to be E-super vertex magic are mCn if and only if both m and n are odd. The article “Marimuthu and Balakrishnan (2012)” discussed the E-super vertex magicness of connected graphs. In this paper, we pay our attention to prove the existence and non existence of E-super vertex magic labeling for some families of disconnected graphs. Also we provide solution to some open problems found in the article “Gray and MacDougall (2009)”.