A quantum graph is connected exactly when its quantum adjacency operator is irreducible, unifying prior definitions and the Laplacian nullity criterion.
↑ [Sta15] Dan Stahlke, Quantum zero-error source-channel coding and non-commutative graph theory, IEEE Trans- actions on Information Theory 62 (2015), no
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Connectivity for quantum graphs via quantum adjacency operators
A quantum graph is connected exactly when its quantum adjacency operator is irreducible, unifying prior definitions and the Laplacian nullity criterion.