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arXiv · 2208.10884

Adjacent Vertex Distinguishing Total Coloring of Corona Product of Graphs

Hanna Furmańczyk·Rita Zuazua
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Abstract

An adjacent vertex distinguishing total $k$-coloring $f$ of a graph $G$ is a proper total $k$-coloring of $G$ such that no pair of adjacent vertices has the same color sets, where the color set at a vertex $v$, $C^G_f(v)$, is $\{f(v)\} \cup \{f(vu)|u \in V (G), vu \in E(G)\}$. In 2005 Zhang et al. posted the conjecture (AVDTCC) that every simple graph $G$ has adjacent vertex distinguishing total $(Δ(G)+3)$-coloring. In this paper we confirm the conjecture for many coronas, in particular for generalized, simple and $l$-coronas of graphs, not relating the results to particular graph classes.

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Hanna Furmańczyk, Rita Zuazua. 2022-08-23. Adjacent Vertex Distinguishing Total Coloring of Corona Product of Graphs. https://arxiv.org/abs/2208.10884

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