In this paper, Boutin introduces new parameters to capture the symmetry of a network. In the last few decades, graph theorists have studied the fewest colors necessary to color the vertices of a network so that no symmetry preserves the coloring. Boutin's new parameters pertain to such colorings that minimize the the number of colors, or the number of vertices with the same color, or (beginning with a neutral coloring) the number of vertices that need recoloring. These parameters both extend and deepen the study of network symmetry.
Debra Boutin, the Samuel F. Pratt Professor of Mathematics, recently published a research article "Paint cost and the frugal distinguishing number," in a special issue of The Art of Discrete and Applied Mathematics.