  The 1-2-3 Conjecture, posed by Karo\'{n}ski, {\L}uczak and Thomason, asked
whether every connected graph $G$ different from $K_2$ can be 3-edge-weighted
so that every two adjacent vertices of $G$ get distinct sums of incident
weights. The 1-2 Conjecture states that if vertices also receive colors and the
vertex color is added to the sum of its incident edges, then adjacent vertices
can be distinguished using only $\{ 1,2\}$. In this paper we confirm 1-2
Conjecture for 3-regular graphs. Meanwhile, we show that every 3-regular graph
can achieve a neighbor sum distinguishing edge coloring by using 4 colors,
which answers 1-2-3 Conjecture positively.
