Quantum / CONCEPT
The complete graph maximizes the trace of the average mixing matrix
For every n and every connected graph G on n vertices, the trace of the average mixing matrix of the adjacency quantum walk on G is at most that of the complete graph K_n. This proves Conjecture 9.1 of C. Godsil, K. Guo and M. Sobchuk (arXiv:1910.02039), read over connected graphs.
Closed
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The complete graph attains the maximum
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Certified topology / UPSTREAM
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RELATED KNOWLEDGE
Structural connections
- Fixed resistance does not force an invariant Fiedler maximizerstructural-affinity · Closed
- Infinitely many non-star trees admit Laplacian peak state transferstructural-affinity · Closed
- Strong cospectrality does not satisfy the general multiplicity boundstructural-affinity · Closed
- The discriminant clears average mixing denominatorsstructural-affinity · Closed
- The star bound for the least-energy uniform overlap failsstructural-affinity · Closed
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