联图C_n∨K_(n-3,n)的全染色

Total Colorings of Join Graph C_n∨K_(n-3,n)

Vizing和Behazd独立地提出了著名的全染色猜想(TCC):任何最大度为Δ的简单图都是Δ+2全可染的.文章通过图的边染色来探究图的全染色,证明了联图G=Cn∨Kn-3,n不仅满足全染色猜想,而且还是第一型的,即χ″(G)=Δ(G)+1.

Vizing and Behazd independently conjectured that every simple graph with maximum degree Δ is Δ＋2 totally colorable. In this paper,we explore the graph edge coloring through the whole graph coloring and prove that the graph G = C n ∨ K n-3,n not only satisfies TCC,but also belongs to the first type,that is χ″（G） = Δ（G） ＋ 1 .