General Vertex-Distinguishing Total Coloring of Graphs

[摘要] The general vertex-distinguishing total chromatic number of a graphGis the minimum integerk, for which the vertices and edges ofGare colored usingkcolors such that any two vertices have distinct sets of colors of them and their incident edges. In this paper, we figure out the exact value of this chromatic number of some special graphs and propose a conjecture on the upper bound of this chromatic number.

[学科分类] 应用数学