The Smarandachely adjacent-vertex distinguishing total coloring of two kind of 3-regular graphs

The Smarandachely adjacent-vertex distinguishing total coloring of graphs is a proper k-total coloring such that every adjacent vertex coloring set not embrace each other, the minimal number k is denoted the Smarandachely adjacent-vertex distinguishing total coloring chromatic number of graphs. Where the coloring set include the colors of all edges incident to the vertex plus the color of it. In this paper, we construct two kind of 3-regular graph R n 3 and S 4n 3 , and obtain the Smarandachely adjacent-vertex distinguishing total coloring chromatic number of it.