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- Debra L. Boutin
- Electr. J. Comb.
- 2006

A set of vertices S is a determining set for a graph G if every automorphism of G is uniquely determined by its action on S. The determining number of a graph is the size of a smallest determining set. This paper describes ways of finding and verifying determining sets, gives natural lower bounds on the determining number, and shows how to use orbits to… (More)

- Michael O. Albertson, Debra L. Boutin
- Electr. J. Comb.
- 2007

This work introduces the technique of using a carefully chosen determining set to prove the existence of a distinguishing labeling using few labels. A graph G is said to be d-distinguishable if there is a labeling of the vertex set using 1,. .. , d so that no nontrivial automorphism of G preserves the labels. A set of vertices S ⊆ V (G) is a determining set… (More)

A set of points W in Euclidean space is said to realize the nite group G if the isometry group of W is isomorphic to G. We show that every nite group G can be realized by a nite subset of some R n , with n < jGj. The minimum dimension of a Euclidean space in which G can be realized is called its isometry dimension. We discuss the isometry dimension of small… (More)

- Debra L. Boutin
- Journal of Graph Theory
- 2009

A set S of vertices is a determining set for a graph G if every auto-morphism of G is uniquely determined by its action on S. The determining number of G, denoted Det(G), is the size of a smallest determining set. This paper begins by proving that if G = G k 1 1 2 · · · 2 G km m is the prime factor decomposition of a connected graph then Det(G) = max{Det(G… (More)

- A-C Desbois, B Wechsler, +5 authors D Saadoun
- La Revue de medecine interne
- 2002

Vascular involvement is a common complication of Behçet's disease (BD) and affects up to 40% of BD patients. These complications worsen the prognosis of BD. The concept of vasculo-Behçet has been adopted for cases in which vascular complications dominate the clinical features. Vascular manifestations affect particularly young men, during the first years… (More)

- Michael O. Albertson, Debra L. Boutin
- Journal of Graph Theory
- 2006

We begin the study of distinguishing geometric graphs. Let G be a geometric graph. An automorphism of the underlying graph that preserves both crossings and noncrossings is called a geometric automorphism.distinguishing if no nontrivial geometric automorphism preserves the labels. The distinguishing number of G is the minimum r such that G has an… (More)

- Michael O. Albertson, Debra L. Boutin
- Discrete & Computational Geometry
- 2008

Let G denote a geometric graph. In particular, V (G) is a set of points in general position in R 2 and the edge uv ∈ E(G) is the straight line segment joining the corresponding pair of points. Two edges, say uv and xy, are said to cross if the interiors of the line segments from u to v and x to y have nonempty intersection. A bijection from V (G) to itself… (More)

- Debra L. Boutin, Ellen Gethner, Thom Sulanke
- Journal of Graph Theory
- 2008

The purpose of this paper is to offer new insight and tools toward the pursuit of the largest chromatic number in the class of thickness-two graphs. At present, the highest chromatic number known for a thickness-two graph is 9, and there is only one known color-critical 1 such graph. We introduce 40 small 9-critical thickness-two graphs, and then use a new… (More)

- Debra L. Boutin
- Graphs and Combinatorics
- 2009

A subset U of vertices of a graph G is called a determining set if every automorphism of G is uniquely determined by its action on the vertices of U. A subset W is called a resolving set if every vertex in G is uniquely determined by its distances to the vertices of W. Determining (resolving) sets are said to have the exchange property in G if whenever S… (More)