摘要： Let f be a proper total k-coloring of a simple graph G. For any vertex x∈V(G), let Cf(x)denote the set of colors assigned to vertex x and the edges incident with x. If Cf(u)=Cf(v)for all distinct vertices u and v of V(G), then f is called a vertex-distinguishing total k-coloring of G. The minimum number k for which there exists a vertex-distinguishing total k-coloring of G is called the vertex-distinguishing total chromatic number of G and denoted by χvt(G). The vertex-disjoint union of two cycles of length n is denoted by 2Cn.We will obtain χvt(2Cn) in this paper.
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