Incidence-adjacent vertex distinguishing equitable total coloring of some Mycielski graphs

DOI：10.7511/dllgxb201805016

 作者 单位 张婷,朱恩强,赵双柱,杜佳

图G的一个邻点可区别Ⅰ-均匀全染色是指对图G的邻点可区别的一个Ⅰ-全染色f，若f还满足Ti－Tj≤1(i≠j)，其中Ti=Vi∪Ei={vv∈V(G)，f(v)=i}∪{ee∈E(G)，f(e)=i}，则称f为图G的一个邻点可区别Ⅰ-均匀全染色，而图G的邻点可区别Ⅰ-均匀全染色中所用的最少颜色数称为图G的邻点可区别Ⅰ-均匀全色数．通过函数构造法，得到了M(Pn)、M(Cn)、M(Sn)的邻点可区别Ⅰ-均匀全色数，并且满足猜想．

The incidence-adjacent vertex distinguishing equitable total coloring of graph Gis that to the incidence-adjacent vertex distinguishing total coloring fof graph G, if fsatisfies Ti－T j≤1 (i≠j), where Ti=Vi∪Ei={vv∈V(G), f(v)=i}∪{ee∈E(G), f(e)=i}, then fis called the incidence-adjacent vertex distinguishing equitable total coloring of graph G. The minimum number of colors required in incidence-adjacent vertex distinguishing equitable total coloring is called incidence-adjacent vertex distinguishing equitable total chromatic number of graph G. The incidence-adjacent vertex distinguishing equitable total chromatic numbers of M(Pn), M(Cn), M(Sn) are obtained by function construction methods, which meet the suspect.