Geodesic
Distinguishing graphs of maximum valence 3
Svenja Hüning1 ; Wilfried Imrich2 ; Judith Kloas1 ; Hannah Schreber1 ; Thomas W. Tucker3
1Graz University of Technology, 8010 Graz, Austria
2Montanuniversität Leoben, 8700 Leoben, Austria
3Colgate University
The electronic journal of combinatorics, Tome 26 (2019) no. 4
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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.
DOI : 10.37236/7281
Classification : 05C07, 05C40, 05C15, 05C63
Mots-clés : distinguishing number, \(2\)-distinguishable graphs

Svenja Hüning  1   ; Wilfried Imrich  2   ; Judith Kloas  1   ; Hannah Schreber  1   ; Thomas W. Tucker  3

1 Graz University of Technology, 8010 Graz, Austria
2 Montanuniversität Leoben, 8700 Leoben, Austria
3 Colgate University 
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     author = {Svenja H\"uning and Wilfried Imrich and Judith Kloas and Hannah Schreber and Thomas W. Tucker},
     title = {Distinguishing graphs of maximum valence 3},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {4},
     doi = {10.37236/7281},
     zbl = {1428.05063},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7281/}
}
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Svenja Hüning; Wilfried Imrich; Judith Kloas; Hannah Schreber; Thomas W. Tucker. Distinguishing graphs of maximum valence 3. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/7281

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