${\chi }_D(G)$, $|Aut(G)|$, and a variant of the Motion Lemma

Niranjan Balachandran, Sajith Padinhatteeri

The \textit{Distinguishing Chromatic Number} of a graph $G$, denoted ${\chi }_D(G)$, was first defined in \cite{collins} as the minimum number of colors needed to properly color $G$ such…