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Paint cost spectrum of perfect $k$-ary trees
We determine the paint cost spectrum for perfect $k$-ary trees. A coloring of the vertices of a graph $G$ with $d$ colors is said to be \emph{$d$-distinguishing} if only the trivial automorphism preserves the color classes. The smallest such $d$ is the distinguishing number of $G$ and is denoted $\mbox{dist}(G).$ …