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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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