Fijavž, Gašper; Negami, Seiya; Sano, Terukazu 3-connected planar graphs are 5-distinguishing colorable with two exceptions. (English) Zbl 1236.05081 Ars Math. Contemp. 4, No. 1, 165-175 (2011). Summary: A graph \(G\) is said to be \(d\)-distinguishing colorable if there is a \(d\)-coloring of \(G\) such that no automorphism of \(G\) except the identity map preserves colors. We shall prove that every 3-connected planar graph is 5-distinguishing colorable except \(K_{2,2,2}\) and \(C_6 + \overline {K_2}\) and that every 3-connected bipartite planar graph is 3-distinguishing colorable except \(Q_3\) and \(R(Q_3)\). Cited in 3 Documents MSC: 05C15 Coloring of graphs and hypergraphs 05C10 Planar graphs; geometric and topological aspects of graph theory Keywords:planar graphs; distinguishing number; distinguishing chromatic number PDFBibTeX XMLCite \textit{G. Fijavž} et al., Ars Math. Contemp. 4, No. 1, 165--175 (2011; Zbl 1236.05081) Full Text: DOI