Neighbor sum distinguishing total chromatic number of planar graphs

Let G = (V(G), E(G)) be a graph and ϕ be a proper k-total coloring of G. Set fϕ(v)=∑uv∈E(G)ϕ(uv)+ϕ(v), for each v ∈ V(G). If fϕ(u) ≠ fϕ(v) for each edge uv ∈ E(G), the coloring ϕ is called a k-neighbor sum distinguishing total coloring of G. The smallest integer k in such a coloring of G is the neig...

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Bibliographic Details
Published in:Applied mathematics and computation 2018-09, Vol.332, p.189-196
Main Authors: Xu, Changqing, Li, Jianguo, Ge, Shan
Format: Article
Language:English
Subjects:
Combinatorial Nullstellensatz
Neighbor sum distinguishing total chromatic number
Planar graph
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Summary:Let G = (V(G), E(G)) be a graph and ϕ be a proper k-total coloring of G. Set fϕ(v)=∑uv∈E(G)ϕ(uv)+ϕ(v), for each v ∈ V(G). If fϕ(u) ≠ fϕ(v) for each edge uv ∈ E(G), the coloring ϕ is called a k-neighbor sum distinguishing total coloring of G. The smallest integer k in such a coloring of G is the neighbor sum distinguishing total chromatic number, denoted by χΣ″(G). In this paper, by using the famous Combinatorial Nullstellensatz, we determine χΣ″(G) for any planar graph G with Δ(G) ≥ 13.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2018.03.013