### Abstract

_{c}k⌉ are fixed by any color preserving automorphism, and that one can do much better in many cases.

Original language | English |
---|---|

Journal | The Australasian Journal of Combinatorics |

Publication status | Submitted - 2018 |

### Fingerprint

### Cite this

**Distinguishing locally finite trees.** / Schreiber, Hannah; Hüning, Svenja; Kloas, Judith; Imrich, Wilfried; Tucker, Thomas.

Research output: Contribution to journal › Article › Research › peer-review

*The Australasian Journal of Combinatorics*.

}

TY - JOUR

T1 - Distinguishing locally finite trees

AU - Schreiber, Hannah

AU - Hüning, Svenja

AU - Kloas, Judith

AU - Imrich, Wilfried

AU - Tucker, Thomas

PY - 2018

Y1 - 2018

N2 - The distinguishing number D(G) of a graph G is the smallest number of colors that is needed to color the vertices of G such that the only color preserving automorphism is the identity. For infinite graphs D(G) is bounded by the supremum of the valences, and for finite graphs by Δ(G)+1, where Δ(G) is the maximum valence. Given a finite or infinite tree T of bounded finite valence k and an integer c, where 2≤c≤k, we are interested in coloring the vertices of T by c colors, such that every color preserving automorphism fixes as many vertices as possible. In this sense we show that there always exists a c-coloring for which all vertices whose distance from the next leaf is at least ⌈logck⌉ are fixed by any color preserving automorphism, and that one can do much better in many cases.

AB - The distinguishing number D(G) of a graph G is the smallest number of colors that is needed to color the vertices of G such that the only color preserving automorphism is the identity. For infinite graphs D(G) is bounded by the supremum of the valences, and for finite graphs by Δ(G)+1, where Δ(G) is the maximum valence. Given a finite or infinite tree T of bounded finite valence k and an integer c, where 2≤c≤k, we are interested in coloring the vertices of T by c colors, such that every color preserving automorphism fixes as many vertices as possible. In this sense we show that there always exists a c-coloring for which all vertices whose distance from the next leaf is at least ⌈logck⌉ are fixed by any color preserving automorphism, and that one can do much better in many cases.

M3 - Article

JO - The Australasian Journal of Combinatorics

JF - The Australasian Journal of Combinatorics

SN - 1034-4942

ER -