Geodesic
3-Connected planar graphs are 5-distinguishing colorable with two exceptions
Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 165-175.

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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 K2,2,2 and C6 + overline(K)2 and that every 3-connected bipartite planar graph is 3-distinguishing colorable except Q3 and R(Q3).
DOI : 10.26493/1855-3974.199.a0e
Keywords: planar graphs, distinguishing number, distinguishing chromatic number 
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Gašper Fijavž; Seiya Negami; Terukazu Sano. 3-Connected planar graphs are 5-distinguishing colorable with two exceptions. Ars Mathematica Contemporanea, Tome 4 (2011) no. 1, pp. 165-175. doi : 10.26493/1855-3974.199.a0e. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.199.a0e/

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