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)
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)
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)
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)
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)
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)
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)
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)