On the Vertex Strong Total Coloring of Graphs
Jingfa Liu · Journal of Hengyang Normal University · 2006
A proper k-total coloring σ of graph G(V,E)is called a k-vertex strong total coloring of G(V,E)if and only if for ν∈V(G),the elements in N[ν]are colored with different colors,where N[ν]={u|νu∈E(G)}∪{ν};and χ~(νs)_(_T)(G)=min{k|there is a k-vertex strong total coloring of G}is called the vertex strong total chromatic number of G.We have obtained the vertex strong total chromatic unmber χ~(νs)_(_T)(G)of some special graphs and present a conjecture:For simple graph G,has k(G)≤χ~(νs)_(_T)(G)≤k(G)+1,where k(G)is a new parameter of G(V,E)defined in this paper.