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Associate Professors of Mathematics Debra Boutin and Sally Cockburn presented their joint work in a pair of talks at the Canadian Discrete and Algorithmic Mathematics Conference at the University of Montreal in May.

Associate Professor of Mathematics Debra Boutin gave an invited address at Discrete Mathematics Day at Bard College on Nov 8. In her talk, Boutin surveyed recent results about the determining set - a small set of nodes that captures all the symmetries of a network. Along with recent findings in various families of networks, Boutin highlighted work showing when minimal determining sets have minimum size, and gave new uses for determining sets in solving other network problems.

Associate Professor of Mathematics Debra Boutin presented a talk titled "The Cost of 2-Distinguishing" at a graph theory conference at Sandbjerg Manor, Denmark. In her talk, Boutin described a set of vertices that can be used to disrupt all symmetries in a network and presented her results on how small these sets of vertices can be in some well-known network families.

Associate Professor of Mathematics Debra Boutin recently published a research article, "Automorphisms and Distinguishing Numbers of Geometric Cliques," in Discrete and Computational Geometry with co-author Michael Albertson. In this paper Boutin and her co-author give conditions under which the symmetries of a maximally connected geometric network can be removed by labeling its vertices using only two labels.

Associate Professor of Mathematics Debra Boutin presented a talk titled "Distinguishing Classes" at the Society for Industrial and Applied Mathematics (SIAM) Conference on Discrete Mathematics held at the University of Vermont, June 16-19. In her talk, Boutin described a set of vertices that can be used to remove all symmetries from a network and presented her results on how surprisingly small these sets of vertices can be in some well-known network families.

Associate Professor of Mathematics Debra Boutin gave a talk titled "Determining Sets, Resolving Sets, and the Exchange Property" at a section meeting for the Society for Industrial and Applied Mathematics (SIAM) held at the University of Central Florida March 14-15. In her talk Boutin described two types of subsets of a network that capture its symmetries. Further she discussed when such subsets are analogous to a basis, a set that is fundamental to other areas of mathematics.

Associate Professor of Mathematics Debra Boutin recently published a research article "Thickness-Two Graphs Part One: New Nine-Critical Graphs, Permuted Layer Graphs, and Catlin's Graphs" in the Journal of Graph Theory with co-authors Ellen Gethner, the University of Colorado at Denver, and Thom Sulanke, Indiana University. A graph (or network drawing) is called thickness-two if it can be drawn in two layers in which neither layer has edges that cross. The thickness of a network is important in computer chip design. In this paper Boutin and her co-authors give new progress on an old problem concerning thickness-two graphs.

Associate Professor of Mathematics Debra Boutin gave a talk at the second Smith College Alumnae Mathematics Conference. The purpose of the conference is to celebrate the 70 plus alumnae who have earned Ph.D.s in the mathematical sciences, the 20 plus who are currently in graduate programs, and the current students who may follow this path. In her talk, Boutin surveyed her recent work on finding a small set of vertices that captures all of a graph's symmetries.

Associate Professor of Mathematics Debra Boutin presented a talk titled "Measuring Graph Symmetry with Determining Sets" at the 1st Canadian Discrete and Algorithmic Mathematics Conference in Banff, Alberta, Canada. Boutin's work focuses on finding a smallest set of nodes that captures all the symmetries in a network. In this talk Boutin gave upper and lower bounds on the size of such a set when the network is presented with a particular decomposition.

Associate Professor of Mathematics Debra Boutin recently published a research article "Structure and Properties of Locally Outerplanar Graphs" in the Journal of Combinatorial Mathematics and Combinatorial Computing. Boutin's paper investigates graphs (network diagrams) that can be drawn in the plane with their vertices on a circle and which contain no short self-intersecting path.