Debra L. Boutin

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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)
A set S of vertices 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 G, denoted Det(G), is the size of a smallest determining set. This paper begins by proving that if G = G1 1 2 · · ·2 Gkm m is the prime factor decomposition of a connected graph then Det(G) = max{Det(Gi i )}.(More)
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(More)
Yu.A. Litvinov1,2, F. Bosch1, H. Geissel1,2, N. Winckler1,2, D. Boutin1,2, H.G. Essel1, T. Faestermann3, S. Hess1, P. Kienle3,4, R. Knöbel1,2, C. Kozhuharov1, J. Kurcewicz1, L. Maier3, K. Beckert1, P. Beller∗1, C. Brandau1, L. Chen2, C. Dimopoulou1, B. Fabian2, A. Fragner4, E. Haettner2, M. Hausmann5, S.A. Litvinov1,2, M. Mazzocco1,6, F. Montes1,5, A.(More)
A graph has thickness t if the edges can be decomposed into t and no fewer planar layers. We study one aspect of a generalization of Ringel’s famous Earth-Moon problem: what is the largest chromatic number of any thickness-2 graph? In particular, given a graph G we consider the r-inflation of G and find bounds on both the thickness and the chromatic number(More)
This paper studies convex geometric graphs in which no path of length 3 self-intersects. A main result gives a decomposition of such graphs into induced outerplanar graph drawings. The resulting structure theorem is then used to compute a sharp, linear upper bound on the size of the edge set in terms of the number of vertices and the number and type of(More)
C. Scheidenberger, I. A. Pshenichnov, K. Sümmerer, A. Ventura, J. P. Bondorf, A. S. Botvina, I. N. Mishustin, D. Boutin, S. Datz,* H. Geissel, P. Grafström, H. Knudsen, H. F. Krause, B. Lommel, S. P. Møller, G. Münzenberg, R. H. Schuch, E. Uggerhøj, U. Uggerhøj, C. R. Vane, Z. Z. Vilakazi, and H. Weick GSI, Planckstraße 1, D-64291 Darmstadt, Germany Niels(More)
Nurses from a CLSC in Hull, Quebec are defining a positive role for community health nurses in a multidisciplinary environment. They base their professional day-to-day practice on Orem's conceptual nursing framework. Many of these home care nurses studied in a post-RN baccalaureate nursing program at the University of Quebec in Hull, where they learned(More)