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The adjacent vertex distinguishing total coloring of planar graphs. (English) Zbl 1319.90076
Summary: An adjacent vertex distinguishing total coloring of a graph $$G$$ is a proper total coloring of $$G$$ such that any pair of adjacent vertices have distinct sets of colors. The minimum number of colors needed for an adjacent vertex distinguishing total coloring of $$G$$ is denoted by $$\chi''_{a}(G)$$.
In this paper, we characterize completely the adjacent vertex distinguishing total chromatic number of planar graphs $$G$$ with large maximum degree $$\varDelta$$ by showing that if $$\varDelta \geq 14$$, then $$\varDelta+1\leq \chi''_{a}(G)\leq \varDelta+2$$, and $$\chi''_{a}(G)=\varDelta+2$$ if and only if $$G$$ contains two adjacent vertices of maximum degree.

##### MSC:
 90C35 Programming involving graphs or networks 05C15 Coloring of graphs and hypergraphs
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##### References:
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