Neighbour sum distinguishing edge-weightings with local constraints

arxiv（2023）

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摘要

A k-edge-weighting of G is a mapping ω:E(G)⟶{1,…,k}. The edge-weighting of G naturally induces a vertex-colouring σω:V(G)⟶N given by σω(v)=∑u∈NG(v)ω(vu) for every v∈V(G). The edge-weighting ω is neighbour sum distinguishing if it yields a proper vertex-colouring σω, i.e., σω(u)≠σω(v) for every edge uv of G.

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关键词

1-2-3 conjecture,Neighbour sum distinguishing edge-weighting,Neighbour sum distinguishing edge-colouring

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