### 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) ≥ C_{1}n^{1/k}, where n is the order of G. We prove c(G) ≤ C_{2}n^{1/k}, and for k = 2, c(G)≤ 9/√2 √n+C.

Original language | English |
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Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Annals of Discrete Mathematics |

Volume | 52 |

Issue number | C |

DOIs | |

Publication status | Published - 1992 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*Annals of Discrete Mathematics*,

*52*(C), 1-9. https://doi.org/10.1016/S0167-5060(08)70896-3

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

Research output: Contribution to journal › Article

*Annals of Discrete Mathematics*, vol. 52, no. C, pp. 1-9. https://doi.org/10.1016/S0167-5060(08)70896-3

}

TY - JOUR

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

AU - Aigner, M.

AU - Triesch, E.

AU - Tuza, Z.

PY - 1992

Y1 - 1992

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.

UR - http://www.scopus.com/inward/record.url?scp=0347252709&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347252709&partnerID=8YFLogxK

U2 - 10.1016/S0167-5060(08)70896-3

DO - 10.1016/S0167-5060(08)70896-3

M3 - Article

AN - SCOPUS:0347252709

VL - 52

SP - 1

EP - 9

JO - Annals of Discrete Mathematics

JF - Annals of Discrete Mathematics

SN - 0167-5060

IS - C

ER -