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If for each $v\\in V(G)$ we have a list $L(v)$ of colors, and we stipulate that the color assigned to vertex $v$ comes from its list $L(v)$ then $G$ is said to be $\\mathcal{L}$-distinguishable where $\\mathcal{L} =\\{L(v)\\}_{v\\in V(G)}$. 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