Symmetry Parameters of Two-Generator Circulant Graphs

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 releva...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Cockburn, Sally, Loeb, Sarah
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.08.2024
Subjects
Automorphisms
Electric potential
Graphs
Subdivisions
Voltage
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2331-8422