Neighbor sum distinguishing total chromatic number of planar graphs

Changqing Xu, Jianguo Li and Shan Ge

Applied Mathematics and Computation, 2018, vol. 332, issue C, 189-196

Abstract: 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.

Keywords: Neighbor sum distinguishing total chromatic number; Combinatorial Nullstellensatz; Planar graph (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:332:y:2018:i:c:p:189-196

DOI: 10.1016/j.amc.2018.03.013

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