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Hidden Symmetries in Simple Graphs

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Author(s): Allen D. Parks

Journal: Symmetry
ISSN 2073-8994

Volume: 4;
Issue: 1;
Start page: 219;
Date: 2012;
Original page

Keywords: graph theory | automorphism group | normalizer | hidden symmetry | symmetry measures

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.
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