C_m∨C_n,C_m∨W_n,C_m∨F_n的点可区别Ⅰ-全染色和点可区别Ⅵ-全染色

Vertex-distinguishing Ⅰ-total Colorings and Vertex-distinguishing Ⅵ-total Colorings of C_m∨C_n,C_m∨W_n,C_m∨F_n

利用构造具体染色的方法,讨论了圈与圈、圈与轮以及圈与扇的联图的点可区别Ⅰ-全染色和点可区别Ⅵ-全染色问题,确定了这3类图的点可区别Ⅰ-全色数和点可区别Ⅵ-全色数,同时说明了VDITC(Vertex-distinguishingⅠ-total colorings)猜想和VDVITC(Vertex-distinguishingⅥ-total colorings)猜想对于这三类图是成立的.

In this paper,we consider the vertex-distinguishing Ⅰ-total colorings and vertex-distinguishing Ⅵ-total colorings of the join of a cycle and a cycle,a cycle and a wheel and a cycle and a fan.By constructing concrete colorings,we determine the vertex-distinguishing Ⅰ-total chromatic numbers and vertex-distinguishing Ⅵ-total chromatic numbers of the abovementioned three families of graphs.Results in this paper illustrate that the VDITC conjecture and VDVITC conjecture are valid for these graphs.