广义Mycielski图M_(n)(P_(t))的邻点可区别的I-均匀全染色

Incidence-Adjacent Vertex Distinguishing Equitable Total Coloring of General Mycielski Graphs of M_(n)(P_(t))

根据路的第一类广义Mycielski图M_(n)(P_(t))的结构特征,运用函数构造法研究并给出了这类图的邻点可区别的I-均匀全染色方法和邻点可区别的I-均匀全色数.特别的,当t>3时,针对路的第一类广义Mycielski图,分n=0(mod 5),n=1(mod 5),…,n=4(mod 5)5种情况讨论并给出了其邻点可区别的I-均匀全色数,所得结果验证了这类图满足邻点可区别I-均匀全染色猜想.

According to the structural characteristics of the first general Mycielski graphs of path,the coloring methods and the chromatic numbers of the incidence-adjacent vertex distinguishing equitable total coloring of the first types of general Mycielski graphs of path were researched and obtained by function construction method.Particularly,when t>3,the incidence-adjacent vertex distinguishing equitable total coloring were discussed in five cases n=0(mod 5),n=2(mod 5),…,n=4(mod 5).The results verified that this kind of graphs satisfied the AVDETC conjecture.