Graphs with Large Distinguishing Chromatic Number (original) (raw)

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Keywords: Distinguishing chromatic number, Distinguishing number, Graph Colouring, Graph automorphism

Abstract

The distinguishing chromatic number chiD(G)\chi_D(G)chiD(G) of a graph GGG is the minimum number of colours required to properly colour the vertices of GGG so that the only automorphism of GGG that preserves colours is the identity. For a graph GGG of order nnn, it is clear that 1leqchiD(G)leqn1\leq\chi_D(G)\leq n1leqchiD(G)leqn, and it has been shown that chiD(G)=n\chi_D(G)=nchiD(G)=n if and only if GGG is a complete multipartite graph. This paper characterizes the graphs GGG of order nnn satisfying chiD(G)=nāˆ’1\chi_D(G)=n-1chiD(G)=nāˆ’1 or chiD(G)=nāˆ’2\chi_D(G)=n-2chiD(G)=nāˆ’2.

How to Cite

Cavers, M., & Seyffarth, K. (2013). Graphs with Large Distinguishing Chromatic Number. The Electronic Journal of Combinatorics, 20(1), #P19. https://doi.org/10.37236/2407