|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||Abstract:||
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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