Authors: Vučković, Bojan 
Title: An improved upper bound on the adjacent vertex distinguishing total chromatic number of graphs
Journal: Discrete Mathematics
Volume: 341
Issue: 5
First page: 1472
Last page: 1478
Issue Date: 1-May-2018
Rank: M22
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.10.011
An adjacent vertex distinguishing total k-coloring of a graph G is a proper total k-coloring of G such that any pair of adjacent vertices have different sets of colors. The minimum number k needed for such a total coloring of G is denoted by χa′′(G). In this paper we prove that χa′′(G)≤2Δ(G)−1 if Δ(G)≥4, and χa′′(G)≤⌈[Formula presented]⌉ in general. This improves a result in Huang et al. (2012) which states that χa′′(G)≤2Δ(G) for any graph with Δ(G)≥3.
Keywords: Adjacent vertex distinguishing total coloring | Maximum degree
Publisher: Elsevier
Project: Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 

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