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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
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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).

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

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