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; in revised form: 23 February 2012 / Accepted: 27 February 2012 / Published: 5 March 2012
PDF Full-text Download PDF Full-Text [197 KB, uploaded 5 March 2012 15:54 CET]
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

Article Statistics

Load and display the download statistics.

Citations to this Article

Cite This Article

MDPI and ACS Style

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

AMA Style

Parks AD. Hidden Symmetries in Simple Graphs. Symmetry. 2012; 4(1):219-224.

Chicago/Turabian Style

Parks, Allen D. 2012. "Hidden Symmetries in Simple Graphs." Symmetry 4, no. 1: 219-224.

Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert