Distinguishing graphs of maximum valence 3

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

doi:10.37236/7281

Distinguishing graphs of maximum valence 3

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

Institute of Geometry (5070)

Research output: Contribution to journal › Article › peer-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 language	English
Article number	P.4.36
Number of pages	27
Journal	The Electronic Journal of Combinatorics
Volume	26
Issue number	4
DOIs	https://doi.org/10.37236/7281
Publication status	Published - 22 Nov 2019

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title = "Distinguishing graphs of maximum valence 3",

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. ",

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AU - Hüning, Svenja

AU - Schreiber, Hannah

AU - Imrich, Wilfried

AU - Kloas, Judith

AU - Tucker, Thomas

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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.

U2 - 10.37236/7281

DO - 10.37236/7281

M3 - Article

SN - 1077-8926

VL - 26

JO - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

IS - 4

M1 - P.4.36

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Distinguishing graphs of maximum valence 3

Abstract

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