Next Article in Journal
Classical Knot Theory
Previous Article in Journal
Self-Dual, Self-Petrie Covers of Regular Polyhedra
Symmetry 2012, 4(1), 219-224; doi:10.3390/sym4010219
Article

Hidden Symmetries in Simple Graphs

Electromagnetic and Sensor Systems Department, 18444 Frontage Road Suite 327, Naval Surface Warfare Center Dahlgren Division, Dahlgren, VA 22448-5161, USA
Received: 15 February 2012 / Revised: 23 February 2012 / Accepted: 27 February 2012 / Published: 5 March 2012
View Full-Text   |   Download PDF [197 KB, uploaded 5 March 2012]

Abstract

It is shown that each element s in the normalizer of the automorphism group Aut(G) of a simple graph G with labeled vertex set V is an Aut(G) invariant isomorphism between G and the graph obtained from G by the s permutation of Vi.e., s is a hidden permutation symmetry of G. A simple example illustrates the theory and the applied notion of system robustness for reconfiguration under symmetry constraint (RUSC) is introduced.
Keywords: graph theory; automorphism group; normalizer; hidden symmetry; symmetry measures graph theory; automorphism group; normalizer; hidden symmetry; symmetry measures
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
SciFeed

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote |
RIS
MDPI and ACS Style

Parks, A.D. Hidden Symmetries in Simple Graphs. Symmetry 2012, 4, 219-224.

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert