Elsevier

Discrete Applied Mathematics

Volume 237, 11 March 2018, Pages 109-115
Discrete Applied Mathematics

Neighbor sum distinguishing total coloring and list neighbor sum distinguishing total coloring

https://doi.org/10.1016/j.dam.2017.12.001Get rights and content
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Abstract

Let χΣt(G) and χΣlt(G) be the neighbor sum distinguishing total chromatic and total choice numbers of a graph G, respectively. In this paper, we present some new upper bounds of χΣlt(G) for -degenerate graphs with integer 1, and of χΣt(G) for 2-degenerate graphs. As applications of these results, (i) for a general graph G, χΣt(G)χΣlt(G)max{Δ(G)+3col(G)21,3col(G)2}, where col(G) is the coloring number of G; (ii) for a 2-degenerate graph G, we determine the exact value of χΣt(G) if Δ(G)6 and show that χΣt(G)7 if Δ(G)5.

Keywords

Neighbor sum distinguishing total coloring
-degenerate
Coloring number
Maximum degree

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