Neighbor Sum Distinguishing Total Choosability of IC-Planar Graphs without Theta Graphs Θ2,1,2
نویسندگان
چکیده
A theta graph Θ2,1,2 is a obtained by joining two vertices three internally disjoint paths of lengths 2, 1, and 2. neighbor sum distinguishing (NSD) total coloring ϕ G proper such that ∑z∈EG(u)∪{u}ϕ(z)≠∑z∈EG(v)∪{v}ϕ(z) for each edge uv∈E(G), where EG(u) denotes the set edges incident with vertex u. In 2015, Pilśniak Woźniak introduced this conjectured every maximum degree Δ admits an NSD (Δ+3)-coloring. paper, we show listing version conjecture holds any IC-planar Δ≥9 but without graphs applying Combinatorial Nullstellensatz, which improves result Song et al.
منابع مشابه
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ژورنال
عنوان ژورنال: Mathematics
سال: 2021
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math9070708