A proper total coloring of the graph G is called D(β)-vertex distinguishing, if any two vertices whose distance is at most β have different color sets, where the color set of a vertex is the set which is composed of all colors of the vertex and the edges incident to it. In this paper, we obtain a new upper bound on D(β)-vertex distinguishing total coloring of a graph.
QIANG Huiying, LI Muchun, ZHANG Zhongfu. A Bound on Vertex Distinguishing Total Coloring of Graphs with Distance Constraint for Recurrent Event Data[J]. Acta Mathematicae Applicatae Sinica, 2011, 34(3): 554-559.