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Neighbor sum distinguishing total coloring of the Halin graph. (Chinese. English summary) Zbl 1363.05078
Summary: Let $$[k]= \{1,2,\dots,k\}$$, a mapping $$\phi$$ is a proper $$[k]$$-total coloring of a graph $$G$$. Let $$f(v)$$ denote the sum of the color of vertex $$v$$ and the colors of the edges incident with $$v$$. A $$[k]$$-neighbor sum distinguishing total coloring of $$G$$ is a $$[k]$$-total coloring of $$G$$ such that for each edge $$uv\in E(G)$$, $$f(u)\neq f(v)$$. Let $$\chi^{\prime\prime}_\Sigma(G)$$ denote the smallest value $$k$$ in such a coloring of $$G$$. There was a conjecture that $$\chi^{\prime\prime}_\Sigma(G)\leq\Delta(G)+3$$ for any simple graph with maximum degree $$\Delta(G)$$. By using the Combinatorial Nullstellensatz, it is shown that the conjecture holds for any Halin graph.
Reviewer: Reviewer (Berlin)

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