两类联图的D(2)-点可区别的全染色

D(2)-Vertex Distinguishing Total Coloring of Graphs

通过对联图S_n∨S_n和F_n∨F_n的D(2)-点可区别的全染色问题的研究,进一步验证了D(β)点可区别的全染色的猜想.利用构造和穷染的方法,给出了图S_n∨S_n和F_n∨F_n的D(2)-点可区别的全染色,得到了图S_n∨S_n和F_n∨F_n的D(2)-点可区别的全色数.

The conjecture on D（β）-vertex distinguishing total coloring of graphs is proved through D （2）-vertex distinguishing total coloring of the join graph of Sn Ⅴ Sn, and FnⅤ Fn. Then, the D（2）-verrex distinguishing total coloring of Sn Ⅴ S,, and Fn Ⅴ F. is given by constructing concrete coloring and exhaustion method, and the D（2）-vertex distinguishing total chromatic number of Sn Ⅴ Sn and FnⅤ Fn, is obtained.