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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; in revised form: 23 February 2012 / Accepted: 27 February 2012 / Published: 5 March 2012
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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 V—i.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
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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.