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View all- Haiman MSchildkraut CZhang SZhao Y(2022)Graphs with high second eigenvalue multiplicityBulletin of the London Mathematical Society10.1112/blms.1264754:5(1630-1652)Online publication date: 16-Apr-2022
Support of closed walks and second eigenvalue multiplicity of graphs
Pages 396 - 407
Abstract
We show that the multiplicity of the second normalized adjacency matrix eigenvalue of any connected graph of maximum degree Δ is bounded by O(n Δ7/5/log1/5−o(1)n) for any Δ, and improve this to O(nlog1/2d/log1/4−o(1)n) for simple d-regular graphs when d≥ log1/4n. In fact, the same bounds hold for the number of eigenvalues in any interval of width λ2/logΔ1−o(1)n containing the second eigenvalue λ2. The main ingredient in the proof is a polynomial (in k) lower bound on the typical support of a closed random walk of length 2k in any connected graph, which in turn relies on new lower bounds for the entries of the Perron eigenvector of submatrices of the normalized adjacency matrix.
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- Support of closed walks and second eigenvalue multiplicity of graphs
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Published In
June 2021
1797 pages
ISBN:9781450380539
DOI:10.1145/3406325
- General Chair:
- Samir Khuller,
- Program Chair:
- Virginia Vassilevska Williams
Copyright © 2021 Owner/Author.
This work is licensed under a Creative Commons Attribution International 4.0 License.
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Association for Computing Machinery
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Published: 15 June 2021
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View all- Haiman MSchildkraut CZhang SZhao Y(2022)Graphs with high second eigenvalue multiplicityBulletin of the London Mathematical Society10.1112/blms.1264754:5(1630-1652)Online publication date: 16-Apr-2022
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