2 problems

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Zhang–Liu–Wang's neighbour set distinguishing index conjecture
Zhang–Liu–Wang's conjecture.
Conjectureopengraph-colourings proper-edge-colourings vertex-distinguishing-colouringsarXiv posted 2 days ago
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The 1–2–3 Conjecture for vertex-distinguishing edge colourings
1–2–3 Conjecture. Every connected graph of order at least $3$ has an edge colouring $c:E\to\{1,2,3\}$ such that $d_c(u)\neq d_c(v)$ for every edge $uv\in E$ .
Conjectureopengraph-colourings vertex-distinguishing-colouringsarXiv posted 2 days ago

Zhang–Liu–Wang's neighbour set distinguishing index conjecture