English

Symmetry Parameters of Two-Generator Circulant Graphs

Combinatorics 2024-08-08 v3

Abstract

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 groups of connected, two-generator circulant graphs, and give their determining and distinguishing number, and when relevant, their cost of 2-distinguishing. We do the same for the subdivisions of connected, two-generator circulant graphs obtained by replacing one loop in the voltage graph with a directed cycle.

Keywords

Cite

@article{arxiv.2305.17504,
  title  = {Symmetry Parameters of Two-Generator Circulant Graphs},
  author = {Sally Cockburn and Sarah Loeb},
  journal= {arXiv preprint arXiv:2305.17504},
  year   = {2024}
}