关键词: 点可区别全染色, 圈, 图的并, 点可区别全色数

Abstract: We considered the problem of the vertexdistinguishing total colorings of the disjoint union mC₇ of m cycles of length 7. By constructing a matrix which was composed of color sets as elements, the vertex distinguishing total coloring of mC₇ was determined by using the methods of distributing color sets in advance and induction. We obtained the exact value of vertexdistinguishing total chromatic number of mC₇. The results show that the VDTC conjecture is valid for mC₇.

Key words: vertexdistinguishing total coloring, vertexdistinguishing total chromatic number, union of graphs, cycle