Super edge magic graceful graphs

A (p,q)(p,q) graph G with p vertices and q   edges is edge magic graceful if there exists a bijection f:V(G)∪E(G)→{1,2,…,p+q}f:V(G)∪E(G)→{1,2,…,p+q} such that |f(u)+f(v)-f(uv)|=k|f(u)+f(v)-f(uv)|=k, a constant for any edge uv of G. G   is said to be super edge magic graceful if f(V(G))={1,2,…,p}f(V(G))={1,2,…,p}. In this paper we present some properties of super edge magic graceful graphs. Using these properties, we prove some classes of graphs are super edge magic graceful. Then we exhibit the relationship between super edge magic graceful labeling and other well studied classes of labelings. In particular, we prove that every super edge magic graceful graph with either f(uv)>f(u)+f(v)f(uv)>f(u)+f(v) for all uv∈E(G)uv∈E(G) or f(uv)