Neighbour sum distinguishing edge-weightings with local constraints
نویسندگان
چکیده
A k-edge-weighting of G is a mapping ω:E(G)⟶{1,…,k}. The edge-weighting naturally induces vertex-colouring σω:V(G)⟶N given by σω(v)=∑u∈NG(v)ω(vu) for every v∈V(G). ω neighbour sum distinguishing if it yields proper σω, i.e., σω(u)≠σω(v) edge uv G. We investigate with local constraints, namely, we assume that the set edges incident to vertex large degree not monochromatic. graph nice has no components isomorphic K2. prove maximum at most 5 admits (Δ(G)+2)-edge-weighting such all vertices least 2 are two different weights. Furthermore, 7-edge-weighting 6 Finally, show bipartite graphs admit 6-edge-weighting
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2023
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2023.04.005