The concept of “Gaussian graceful labeling (or valuation)” is introduced in this paper while labeling graphs. Throughout the paper, we used the Gaussian integers to label the graph. For a graph G to be gracefully labeled with Gaussian integers, for any positive number p, the vertex labeling , z is a Gaussian integer, which lies in the first quadrant and the edge labeling is defined by must both be injective and also there exist such that for any edge of G holds, either . Let us refer to graph G as a Gaussian graceful graph if it permits graceful labeling. We establish a valuation in this study and examine the valuation for some unique type of graphs and family of fan graphs such as