### Abstract

Original language | English |
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Journal | Electronic Journal of Combinatorics |

Publication status | Submitted - 2017 |

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### Cite this

**Distinguishing graphs of maximum valence 3.** / Schreiber, Hannah; Hüning, Svenja; Imrich, Wilfried; Kloas, Judith; Tucker, Thomas.

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

*Electronic Journal of Combinatorics*.

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TY - JOUR

T1 - Distinguishing graphs of maximum valence 3

AU - Schreiber, Hannah

AU - Hüning, Svenja

AU - Imrich, Wilfried

AU - Kloas, Judith

AU - Tucker, Thomas

PY - 2017

Y1 - 2017

N2 - The distinguishing number D(G) of a graph G is the smallest number of colors that is needed to color G such that the only color preserving automorphism is the identity. We give a complete classification for all connected graphs G of maximum valence Δ(G)=3 and distinguishing number D(G)=3. As one of the consequences we get that all infinite connected graphs with Δ(G)=3 are 2-distinguishable.

AB - The distinguishing number D(G) of a graph G is the smallest number of colors that is needed to color G such that the only color preserving automorphism is the identity. We give a complete classification for all connected graphs G of maximum valence Δ(G)=3 and distinguishing number D(G)=3. As one of the consequences we get that all infinite connected graphs with Δ(G)=3 are 2-distinguishable.

M3 - Article

JO - The electronic journal of combinatorics

JF - The electronic journal of combinatorics

SN - 1077-8926

ER -