# Irregular assignments and vertex-distinguishing edge-colorings of graphs

M. Aigner, E. Triesch, Z. Tuza

Research output: Contribution to journalArticle

40 Citations (Scopus)

### Abstract

A coloring g: E(G) →C of the edge-set of a graph G into a color-set C is called vertex-distinguishing if g(St(u)) ≠g(St(v)) for any two stars. Let c(G) be the minimal number of colors necessary for such a coloring. For k-regular graphs G we clearly have c(G) ≥ C1n1/k, where n is the order of G. We prove c(G) ≤ C2n1/k, and for k = 2, c(G)≤ 9/√2 √n+C.

Original language English 1-9 9 Annals of Discrete Mathematics 52 C https://doi.org/10.1016/S0167-5060(08)70896-3 Published - 1992

### Fingerprint

Edge Coloring
Colouring
Irregular
Assignment
Graph in graph theory
Vertex of a graph
Regular Graph
Star
Necessary
Color

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics

### Cite this

Irregular assignments and vertex-distinguishing edge-colorings of graphs. / Aigner, M.; Triesch, E.; Tuza, Z.

In: Annals of Discrete Mathematics, Vol. 52, No. C, 1992, p. 1-9.

Research output: Contribution to journalArticle

title = "Irregular assignments and vertex-distinguishing edge-colorings of graphs",
abstract = "A coloring g: E(G) →C of the edge-set of a graph G into a color-set C is called vertex-distinguishing if g(St(u)) ≠g(St(v)) for any two stars. Let c(G) be the minimal number of colors necessary for such a coloring. For k-regular graphs G we clearly have c(G) ≥ C1n1/k, where n is the order of G. We prove c(G) ≤ C2n1/k, and for k = 2, c(G)≤ 9/√2 √n+C.",
author = "M. Aigner and E. Triesch and Z. Tuza",
year = "1992",
doi = "10.1016/S0167-5060(08)70896-3",
language = "English",
volume = "52",
pages = "1--9",
journal = "Annals of Discrete Mathematics",
issn = "0167-5060",
publisher = "Elsevier",
number = "C",

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T1 - Irregular assignments and vertex-distinguishing edge-colorings of graphs

AU - Aigner, M.

AU - Triesch, E.

AU - Tuza, Z.

PY - 1992

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N2 - A coloring g: E(G) →C of the edge-set of a graph G into a color-set C is called vertex-distinguishing if g(St(u)) ≠g(St(v)) for any two stars. Let c(G) be the minimal number of colors necessary for such a coloring. For k-regular graphs G we clearly have c(G) ≥ C1n1/k, where n is the order of G. We prove c(G) ≤ C2n1/k, and for k = 2, c(G)≤ 9/√2 √n+C.

AB - A coloring g: E(G) →C of the edge-set of a graph G into a color-set C is called vertex-distinguishing if g(St(u)) ≠g(St(v)) for any two stars. Let c(G) be the minimal number of colors necessary for such a coloring. For k-regular graphs G we clearly have c(G) ≥ C1n1/k, where n is the order of G. We prove c(G) ≤ C2n1/k, and for k = 2, c(G)≤ 9/√2 √n+C.

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SP - 1

EP - 9

JO - Annals of Discrete Mathematics

JF - Annals of Discrete Mathematics

SN - 0167-5060

IS - C

ER -