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On the adjacent vertex distinguishing total coloring numbers of graphs with $$\varDelta =3$$. (English) Zbl 1203.05052
Summary: An adjacent vertex distinguishing total-coloring of a simple graph $$G$$ is a proper total-coloring of $$G$$ such that no pair of adjacent vertices meets the same set of colors. The minimum number of colors $$\chi _a ^{\prime \prime}$$ required to give $$G$$ an adjacent vertex distinguishing total-coloring is studied. We proved $$\chi _a ^{\prime \prime}\leqslant 6$$ for graphs with maximum degree $$\varDelta (G)=3$$ in this paper.

##### MSC:
 05C15 Coloring of graphs and hypergraphs
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