Given a graph G consisting of vertices and edges, a vertex labeling of G is an assignment f of labels to the vertices of G that produces for each edge xy a label depending on the vertex labels f (x) and f (y). A vertex labeling f is called a graceful labeling of a graph G with q edges if f is an injection from the vertices of G to the set {0,1,2,...q} such that when each edge xy is assigned the label |f (x)-f (y)| the resulting edge labels are distinct. A graph G is called graceful if there exists a graceful labeling of G (see figure 1). In this Paper we give some results on Central graphs (The Central Graph C(G) of a graph G is obtained by subdividing each edge of G exactly once and joining all the non-adjacent vertices of G (see figure 2)) and gracefulness of Central graphs of Cycles being investigated.