Add to ORKGThe fixing number of a graph is the order of the smallest subset of its vertex set such that assigning distinct labels to all of the vertices in that subset results in the trivial automorphism; this is a recently introduced parameter that provides a measure of the non-rigidity of a graph. We provide a survey of elementary results about fixing numbers. We examine known algorithms for computing the fixing numbers of graphs in general and algorithms which are applied only to trees. We also present and prove the correctness of new algorithms for both of those cases. We examine the distribution of fixing numbers of various classifications of graphs
Determining vertex subsets are known tools to provide information about automorphism groups of graph...
Many modern data analysis algorithms either assume or are considerably more efficient if the distanc...
AbstractSuppose G is a graph without loops or digons and H is a spanning subgraph of G. Let A(G) be ...
The fixing number of a graph G is the smallest cardinality of a set of vertices S such that only the...
AbstractThe fixing number of a graph G is the minimum cardinality of a set S⊂V(G) such that every no...
An automorphism of a graph is a mapping of the vertices onto themselves such that connections betwee...
In this paper we study the complexity of the following problems: 1. Given a colored graph X=(V,E,c)...
Motivated by work in graph theory, we define the fixing number for a matroid. We give upper and lowe...
An automorphism of a graph describes its structural symmetry and the concept of fixing number of a g...
Abstract. A note v of a graph G is called fixed if every automorphism of G sends v onto itself. A gr...
Let G ☐ H denote the Cartesian product of the graphs G and H. In 2004, Hartnell and Rall [On dominat...
One of the most important open questions in graph theory is the graph reconstruction conjecture, fir...
AbstractGiven a planar graph G, we consider drawings of G in the plane where edges are represented b...
Analogous to the fixed point property for ordered sets, a graph has the fixed vertex property if eac...
Abstract. Given a planar graph G, we consider drawings of G in the plane where edges are represented...
Determining vertex subsets are known tools to provide information about automorphism groups of graph...
Many modern data analysis algorithms either assume or are considerably more efficient if the distanc...
AbstractSuppose G is a graph without loops or digons and H is a spanning subgraph of G. Let A(G) be ...
The fixing number of a graph G is the smallest cardinality of a set of vertices S such that only the...
AbstractThe fixing number of a graph G is the minimum cardinality of a set S⊂V(G) such that every no...
An automorphism of a graph is a mapping of the vertices onto themselves such that connections betwee...
In this paper we study the complexity of the following problems: 1. Given a colored graph X=(V,E,c)...
Motivated by work in graph theory, we define the fixing number for a matroid. We give upper and lowe...
An automorphism of a graph describes its structural symmetry and the concept of fixing number of a g...
Abstract. A note v of a graph G is called fixed if every automorphism of G sends v onto itself. A gr...
Let G ☐ H denote the Cartesian product of the graphs G and H. In 2004, Hartnell and Rall [On dominat...
One of the most important open questions in graph theory is the graph reconstruction conjecture, fir...
AbstractGiven a planar graph G, we consider drawings of G in the plane where edges are represented b...
Analogous to the fixed point property for ordered sets, a graph has the fixed vertex property if eac...
Abstract. Given a planar graph G, we consider drawings of G in the plane where edges are represented...
Determining vertex subsets are known tools to provide information about automorphism groups of graph...
Many modern data analysis algorithms either assume or are considerably more efficient if the distanc...
AbstractSuppose G is a graph without loops or digons and H is a spanning subgraph of G. Let A(G) be ...