An equivalence theorem links perfect state transfer between pair states in an involution-equipped graph to transfer in the induced subgraph, enabling explicit constructions for almost all planar graphs, trees, and certain paths via added loops or edges.
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Fractional revival on Γ(ℤ_n) occurs only for size-2 cells in the equitable partition induced by proper divisors of n, with PST possible under a sufficient condition on n and non-existence proven for Γ(ℤ_{p²q}).
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Laplacian state transfer in graphs with involutions
An equivalence theorem links perfect state transfer between pair states in an involution-equipped graph to transfer in the induced subgraph, enabling explicit constructions for almost all planar graphs, trees, and certain paths via added loops or edges.
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Quantum fractional revival on zero-divisor graphs over $\mathbb{Z}_n$
Fractional revival on Γ(ℤ_n) occurs only for size-2 cells in the equitable partition induced by proper divisors of n, with PST possible under a sufficient condition on n and non-existence proven for Γ(ℤ_{p²q}).