若干Mycielski图的邻点扩展和可区别全染色

Neighbor expanded sum distinguishing total coloring of some Mycielski graphs

讨论了Mycielski图M(P_(n))、M(C_(n))、M(S_(n))、M(F_(n))、M(W_(n))的邻点扩展和可区别全染色问题.根据图形的结构特点,采用函数构造法,得到了这几类图的邻点扩展和可区别全色数,同时证明NESD猜想对上述5种Mycielski图是成立的.

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.