Vertex Strongly Distinguishing Total Coloring of Complete Bipartite Graphs K_(1,n),K_(2,n) and K_(3,n)
Xiang Chen · Shuxue de shijian yu renshi · 2012
Let f be a proper total coloring of G.For each x∈V(G),let C(x) denote the set of all colors of the elements incident with or adjacent to x and the color of x.If A u,v∈V(G),u≠v,we have C(u)≠C(v),then / is called a vertex strongly distinguishing total coloring of G.The minimum number k for which there exists a vertex strongly distinguishing total coloring of G using k colors is called the vertex strongly distinguishing total chromatic number of G and denoted byχ_(vst)(G).In this paper,we discuss vertex strongly distinguishing total chromatic numbers of complete bipartite graphs K_(1,n),K_(2,n) and K_(3,n) using methods of combinatorial analysis,obtained thatχ_(vst)(K_(1,n)) = n + 1 when n≥3,χ_(vst)(K_(2,n)) = n + 2 when n≥4,χ_(vst)(K_(3,n)) = n + 2 when n≥5.