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arXiv · 1708.03121

Twins and Vertex- Identification on Graphs

Sylvain Gravier·Simon Schmidt·Souad Slimani
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Abstract

Recently, several vertex identifying notions were introduced (identifying coloring, lid-coloring, ...), these notions were inspired by identifying codes. All of them, as well as original identifying code, are based on separating two vertices according to some conditions on their closed neighborhood. Therefore, twins can not be identified. So most of known results focus on twin-free graph. Here, we show how twins can modify optimal value of vertex-identifying parameters for identifying coloring and locally identifying coloring. \textbf{Keyword :} Identifying coloring, locally identifying coloring, twins, separating.

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Sylvain Gravier, Simon Schmidt, Souad Slimani. 2017-08-10. Twins and Vertex- Identification on Graphs. https://arxiv.org/abs/1708.03121

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