Abstract: Discusses the neighbor expanded sum distinguishing total coloring of Mycielski graphs M(P_n)、M(C_n)、M(S_n)、M(F_n) and M(W_n). The neighbor expanded sum distinguishing total chromatic numbers of M(P_n)、M(C_n)、M(S_n)、M(F_n) and M(W_n) are obtained by function construction methods. At the same time, it is proved that NESD conjecture is valid for the above five kinds of Mycielski graphs.

Key words: Mycielski graph, neighbor expanded sum distinguishing total coloring, neighbor expanded sum distinguishing total chromatic number