Distinguishing graphs of maximum valence 3

Hannah Schreiber, Svenja Hüning, Wilfried Imrich, Judith Kloas, Thomas Tucker

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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.
Original languageEnglish
JournalElectronic Journal of Combinatorics
Publication statusAccepted/In press - 2019

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Color
Connected graph
Graph in graph theory
Infinite Graphs
Automorphism

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Schreiber, H., Hüning, S., Imrich, W., Kloas, J., & Tucker, T. (Accepted/In press). Distinguishing graphs of maximum valence 3. Electronic Journal of Combinatorics.

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

In: Electronic Journal of Combinatorics, 2019.

Research output: Contribution to journalArticleResearchpeer-review

Schreiber, H, Hüning, S, Imrich, W, Kloas, J & Tucker, T 2019, 'Distinguishing graphs of maximum valence 3' Electronic Journal of Combinatorics.
Schreiber H, Hüning S, Imrich W, Kloas J, Tucker T. Distinguishing graphs of maximum valence 3. Electronic Journal of Combinatorics. 2019.
Schreiber, Hannah ; Hüning, Svenja ; Imrich, Wilfried ; Kloas, Judith ; Tucker, Thomas. / Distinguishing graphs of maximum valence 3. In: Electronic Journal of Combinatorics. 2019.
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