Graph disjointness is characterized by spectral overlap of Markov transition matrices and tree structures, depending only on vertex and edge sets rather than weights.
On cycles in the coprime graph of integers.the electronic journal of combinatorics, pages R8–R8, 1997
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Graph Disjointness with Applications to Reversible Markov Chains
Graph disjointness is characterized by spectral overlap of Markov transition matrices and tree structures, depending only on vertex and edge sets rather than weights.