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}
}