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.
|Number of pages||27|
|Journal||The Electronic Journal of Combinatorics|
|Publication status||Published - 22 Nov 2019|