Distinguishing Graphs of Maximum Valence 3

The distinguishing number $D(G)$ of a graph $G$ is the smallest number of colors that is needed to color the vertices such that the only color-preserving automorphism fixes all vertices. We give a complete classification for all connected graphs $G$ of maximum valence $\Delta(G) = 3$ and distinguish...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2019-11, Vol.26 (4)
Main Authors: Hüning, Svenja, Imrich, Wilfried, Kloas, Judith, Schreber, Hannah, Tucker, Thomas W.
Format: Article
Language:English
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Summary:The distinguishing number $D(G)$ of a graph $G$ is the smallest number of colors that is needed to color the vertices such that the only color-preserving automorphism fixes all vertices. We give a complete classification for all connected graphs $G$ of maximum valence $\Delta(G) = 3$ and distinguishing number $D(G) = 3$. As one of the consequences we show that all infinite connected graphs with $\Delta(G) = 3$ are $2$-distinguishable.
ISSN:1077-8926
1077-8926
DOI:10.37236/7281