On the Total Neighbor Sum Distinguishing Index of IC-Planar Graphs
A proper total k-coloring ϕ of G with ∑z∈EG(u)∪{u}ϕ(z)≠∑z∈EG(v)∪{v}ϕ(z) for each uv∈E(G) is called a total neighbor sum distinguishing k-coloring, where EG(u)={uv|uv∈E(G)}. Pilśniak and Woźniak conjectured that every graph with maximum degree Δ exists a total neighbor sum distinguishing (Δ+3)-coloring. In this paper, we proved that any IC-planar graph with Δ≥12 satisfies this conjecture, which improves the result of Song and Xu [J. Comb. Optim., 2020, 39, 293–303].
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2014 ◽
Vol 23
(4)
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pp. 551-570
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2018 ◽
Vol 10
(04)
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pp. 1850044
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