Abstract: he minimum number of colors required to give a graph $G$ an adjacent
vertex-distinguishing edge partition was studied. Based on the classification of the
degree of a graph, this paper proved that every graph without $K_{2}$ of minimum degree
at least 188 permits an adjacent vertex-distinguishing 3-edge partition. The result is
more superior than previous ones.

Key words: adjacent vertex-distinguishing, non-proper , edge partition, adjacent vertex-distinguishing, non-proper