Hidden symmetries in simple graphs (Q350599)

Summary: It is shown that each element \(s\) in the normalizer of the automorphism group \(\mathrm{Aut}(G)\) of a simple graph \(G\) with labeled vertex set \(V\) is an \(\mathrm{Aut}(G)\) invariant isomorphism between \(G\) and the graph obtained from \(G\) by the \(s\) permutation of \(V\) -- i.e., \(\sigma\) 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.