Authors: Vučković, Bojan 
Title: Multi-set neighbor distinguishing 3-edge coloring
Journal: Discrete Mathematics
Volume: 341
Issue: 3
First page: 820
Last page: 824
Issue Date: 1-Mar-2018
Rank: M22
ISSN: 0012-365X
DOI: 10.1016/j.disc.2017.12.001
Let G be a graph without isolated edges, and let c:E(G)→{1,…,k} be a coloring of the edges, where adjacent edges may be colored the same. The color code of a vertex v is the ordered k-tuple (a1,a2,…,ak), where ai is the number of edges incident with v that are colored i. If every two adjacent vertices of G have different color codes, such a coloring is called multi-set neighbor distinguishing. In this paper, we prove that three colors are sufficient to produce a multi-set neighbor distinguishing edge coloring for every graph without isolated edges.
Keywords: Multi-set neighbor distinguishing edge coloring
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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