Elsonbaty and Daoud introduced a new type of labeling called Edge Even Graceful Labeling. He also stated a necessary and sufficient condition for Even Edge Labeling of Path Graphs, Cycle Graphs, Star Graphs, Friendship Graphs, Wheel Graphs, Double Wheel Graphs, and Fan Graphs. In this chapter, we described and studied the concept of Maximum Degree Based Vertex Graceful Labeling Graph with Even labeling on edges. We characterized and illustrated the concept of Maximum Degree Based Vertex Graceful Labeling with Even labeling on Edges