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Neighbor sum distinguishing total chromatic number of 2-degenerate graphs. (English) Zbl 1401.05128
Summary: Let $$G = (V(G), E(G))$$ be a graph and $$\phi$$ be a proper total $$k$$-coloring of $$G$$ by using the color set $$\{1, 2, \ldots, k \}$$. For any $$v \in V(G)$$, let $$f(v) = \sum_{u v \in E(G)} \phi(u v) + \phi(v)$$. The coloring $$\phi$$ is neighbor sum distinguishing, if $$f(u) \neq f(v)$$ for each edge $$u v \in E(G)$$. The neighbor sum distinguishing total chromatic number of $$G$$, denoted by $$\chi_\varSigma^{\prime \prime}(G)$$, is the smallest integer $$k$$ such that $$G$$ admits a $$k$$-neighbor sum distinguishing total coloring. In this paper, by using the famous Combinatorial Nullstellensatz, we determine $$\chi_\varSigma^{\prime \prime}(G)$$ for any 2-degenerate graph $$G$$ with $$\varDelta(G) \geq 6$$.

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