一类含有4-圈的单圈图一般点可区别全染色

General vertex-distinguishing total colorings of a family of unicyclic graphs including C_4

设G为简单图.设f是图G的一个一般全染色,若对图G的任意两个不同的顶点u、v,有C(u)≠C(v),则称f为图G的一般点可区别全染色(简记为GVDTC).对图G进行一般点可区别全染色所需要的最少颜色数称为图G的一般点可区别全色数.将一类含有4-圈的单圈图悬挂边的染色按从小到大的顺序排列,探讨了它的一般点可区别全染色,确定了它具有一般点可区别全染色,并得到了它的一般点可区别全色数.

Let Gbe a simple graph.For a general total coloring fof G,if C（u）≠C（v）for any two different vertices uand v of G,then fis called a general vertex-distinguishing total coloring of G（or GVDTC of Gfor short）.The minimum number of colors required in a GVDTC is the general vertexdistinguishing total chromatic number.The general vertex-distinguishing total colorings of a family of unicyclic graphs including C4 are discussed by making the coloring of its pendent edges in an ascending order.It is determined that it has a general vertex-distinguishing total coloring of Gand its general vertex-distinguishing total chromatic number is got.