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Adjacent vertex distinguishing total colorings of graphs with smaller degrees. (English) Zbl 1313.05142

Summary: In this paper, we study the adjacent vertex distinguishing total colorings of graphs with maximum degree three and no adjacent \(\Delta\)-vertices. By the technique of splitting edges, graphs with more special situations are constructed. We also obtain the upper bound of adjacent vertex distinguishing total chromatic numbers of these graphs. Up to present, a graph having maximum degree three such that its adjacent vertex distinguishing total chromatic number is six has not been reported in current literatures, our conclusion answers this problem partially.

MSC:

05C15 Coloring of graphs and hypergraphs
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