Abstract: By using mathematical induction, reductio ad absurdum as well as construction of specific coloring function, together with Hall theorem, we discussed the D(2)-vertex-distinguishing edge coloring of unicyclic graphs, and gave their precise D(2)-vertex-distinguishing edge chromatic numbers.

Key words: unicyclic graph, edge-coloring, D(2)-vertex-distinguishing edge coloring, D(2)-vertex-distinguishing edge chromatic number