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

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]


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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
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


Cited By

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