We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Finding the Fixing Number of Johnson Graphs J(n, k) for k ∊ {2, 3}.
- Authors
Della-Giustina, James
- Abstract
The graph invariant, aptly named the fixing number, is the smallest number of vertices that, when fixed, eliminate all non-trivial automorphisms (or symmetries) of a graph. Although many graphs have established fixing numbers, Johnson graphs, a family of graphs related to the graph isomorphism problem, have only partially classified fixing numbers. By examining specific orbit sizes of the automorphism group of Johnson graphs and classifying the subsequent remaining subgroups of the automorphism group after iteratively fixing vertices, we provide exact minimal sequences of fixed vertices, in turn establishing the fixing number of infinitely many Johnson graphs.
- Subjects
AUTOMORPHISM groups; PERMUTATION groups; ORBITS (Astronomy); ISOMORPHISM (Mathematics); CAYLEY graphs
- Publication
American Journal of Undergraduate Research, 2023, Vol 20, Issue 3, p81
- ISSN
1536-4585
- Publication type
Article
- DOI
10.33697/ajur.2023.097