Christopher, Peter R.
The 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.
Worcester Polytechnic Institute
Major Qualifying Project
All authors have granted to WPI a nonexclusive royalty-free license to distribute copies of the work, subject to other agreements. Copyright is held by the author or authors, with all rights reserved, unless otherwise noted.