In this paper, we study a new coloring parameter of graphs called the gap vertex-distinguishing edge coloring. It consists in an edge-coloring of a graph which induces a vertex distinguishing labeling of such that the label of each vertex is given by the difference between the highest and the lowest colors of its adjacent edges. The minimum number of colors required for a gap vertex-distinguishing edge coloring of is called the gap chromatic number of and is denoted by .We here study the gap chromatic number for a large set of graphs of order and prove that .