3 citations · 4 across the 10 of their papers we have counts for
11 papers · 1 filter
Symmetry Parameters of Two-Generator Circulant Graphs
Sally Cockburn, Sarah Loeb
The derived graph of a voltage graph consisting of a single vertex and two loops of different voltages is a circulant graph with two generators. We characterize the automorphism gr…
Edge Determining Sets and Determining Index
Sean McAvoy, Sally Cockburn
A graph automorphism is a bijective mapping of the vertices that preserves adjacent vertices. A vertex determining set of a graph is a set of vertices such that the only automorphi…
Symmetry Parameters of Various Hypercube Families
Debra Boutin, Sally Cockburn, Lauren Keough +2
In this paper we study the symmetry parameters determining number, distinguishing number, and cost of 2-distinguishing, for some variations on hypercubes, namely Hamming graphs, po…
Symmetry Parameters for Mycielskian Graphs
Debra Boutin, Sally Cockburn, Lauren Keough +3
The Mycielskian construction, denoted , takes a finite simple graph to a larger graph with of the same clique number but larger chromatic number. The generalized Mycielsk…
Determining Number and Cost of Generalized Mycielskian Graphs
Debra Boutin, Sally Cockburn, Lauren Keough +3
A set of vertices is a determining set for a graph if every automorphism of is uniquely determined by its action on . The size of a smallest determining set for …
Distinguishing Generalized Mycielskian Graphs
Debra Boutin, Sally Cockburn, Lauren Keough +3
A graph is -distinguishable if there is a coloring of the vertices with colors so that only the trivial automorphism preserves the color classes. The smallest such i…
Distinguishing Orthogonality Graphs
Debra Boutin, Sally Cockburn
A graph is said to be -distinguishable if there is a labeling of the vertices with labels so that only the trivial automorphism preserves the labels. The smallest such $…
Homomorphic Preimages of Geometric Cycles
Sally Cockburn
A graph G is a homomorphic preimage of another graph H, or equivalently G is H-colorable, if there exists a graph homomorphism from G to H. A classic problem is to characterize the…
The Homomorphism Poset of
Sally Cockburn
A geometric graph \G is a simple graph drawn in the plane, on points in general position, with straight-line edges. We call \G a geometric realization of the underlying abstract gr…
Posets of Geometric Graphs
Debra L. Boutin, Sally Cockburn, Alice Dean +1
A geometric graph G(bar) is a simple graph drawn in the plane, on points in general position, with straight-line edges. We call G(bar) a geometric realization of the underlying abs…
The Homomorphism Poset of K_{2,n}
Sally Cockburn, Yonghyun Song
A geometric graph is a simple graph G together with a straight line drawing of G in the plane with the vertices in general position. Two geometric realizations of a simple graph ar…