Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-06-27T09:32:43.371239Z
Paper Citation Record · LEDGER
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs
As of 8 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2606.11659.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
50 of 50 outbound references displayed
- verified exact9
- verified fuzzy0
- unresolved41
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 70605f0e-d689-4204-be4d-b475be8d28b3 · outbound
This paper cites Aouchiche, P.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Aouchiche, P
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7966fe8a-4322-4cef-8a2e-f9e0966b11a6 · outbound
This paper cites Bauer and G.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Bauer and G
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2e18b7a8-6898-43a9-9ccb-2e8124143aa8 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a75e862f-15da-425e-a7c7-f8521b171ca1 · outbound
This paper cites Bıyıko˘ glu and J.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Bıyıko˘ glu and J
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b0641aae-cb09-4872-89df-211d19460de9 · outbound
This paper cites Brooks, M.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Brooks, M
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ed7f48ac-86b3-47ef-a81d-7754c2f125e8 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f550d2c7-42c0-4d19-8e74-8e62ff988c54 · outbound
This paper cites Byrne, D.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Byrne, D
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 93710c54-b2a3-47e1-970b-62f7bd343299 · outbound
This paper cites The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs The Quantitative Faber-Krahn Inequality for the Combinatorial Laplacian in $\mathbb{Z}^{d}$
Reference 8
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T11:28:04.527374Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 51859e05-74b7-4c4a-a678-52e46ac85ef1 · outbound
This paper cites Dautenhahn and L.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Dautenhahn and L
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b842e6ca-3a49-44a8-ad8a-99ac805e9c1c · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0478b38b-6010-464d-9a1b-5adb9d13c08c · outbound
This paper cites Favaron, M.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Favaron, M
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6b803cb0-ca13-4f69-8954-c9423802fd73 · outbound
This paper cites Filonov, M.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Filonov, M
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ba2c9944-5805-485f-98a8-9fc4989a09ef · outbound
This paper cites Filonov, M.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Filonov, M
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 33d17adc-4649-4827-ac7a-8a175b72efa8 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1e5bdfdb-d224-4fbd-8ea1-ac62310f5a2f · outbound
This paper cites Freitas, A remark on P´ olya’s conjecture at low frequencies,Arch.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Freitas, A remark on P´ olya’s conjecture at low frequencies,Arch
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f34f70a3-a331-4a49-bd65-a1e650d1aa67 · outbound
This paper cites P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$
Reference 16
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T11:28:04.524575Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e470509b-4cde-4a4d-b692-46ddf85f60a8 · outbound
This paper cites Friedman, Some geometric aspects of graphs and their eigenfunctions,Duke Math.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Friedman, Some geometric aspects of graphs and their eigenfunctions,Duke Math
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 266ea0dd-aaa9-480d-b695-f7dfb317afc2 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3910a995-eb71-4f8e-83db-9d44046c74a8 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9b123818-58e0-438d-9008-b0b2828fffd2 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 20
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T11:28:04.521675Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2a6888c6-2543-4692-834b-e8ca3eb80cff · outbound
This paper cites He and C.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs He and C
Reference 21
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T11:28:04.518796Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 50cdaa72-3926-42da-8c2b-4a60c1ff2bae · outbound
This paper cites He and C.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs He and C
Reference 22
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T11:28:04.516289Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation f6eb2fdc-237a-4ba0-9c88-c883b7c710bd · outbound
This paper cites P\'olya's conjecture for thin products.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs P\'olya's conjecture for thin products
Reference 23
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T11:28:04.509828Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 87e0a2ce-a41c-44b6-ac8b-889f7a0fd45a · outbound
This paper cites Henrot, Extremum problems for eigenvalues of elliptic operators,Frontiers in Math- ematics, Birkh¨ auser, Basel, 2006.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Henrot, Extremum problems for eigenvalues of elliptic operators,Frontiers in Math- ematics, Birkh¨ auser, Basel, 2006
Reference 24
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e26288d8-5048-4727-9021-e558ba4c9d67 · outbound
This paper cites Hong, A bound on the spectral radius of graphs,Linear Algebra Appl.108(1988), 135–139.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Hong, A bound on the spectral radius of graphs,Linear Algebra Appl.108(1988), 135–139
Reference 25
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 039d9cdb-8ec6-45d9-af6f-ef4e540d3ec2 · outbound
This paper cites Hong, Bounds of eigenvalues of a graph,Acta Math.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Hong, Bounds of eigenvalues of a graph,Acta Math
Reference 26
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 18015f87-182d-48c6-bdfd-9e3a09a5f925 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8d7beeb1-34ef-4046-abb1-43e2ca22fc56 · outbound
This paper cites Wang and X.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Wang and X
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ca6ce15c-6052-4544-b063-428e9f1b9ecf · outbound
This paper cites Hua and R.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Hua and R
Reference 29
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ce8c2e63-7aec-4a99-9cc5-7681ae99f207 · outbound
This paper cites P\'olya's conjecture up to $\epsilon$-loss and quantitative estimates for the remainder of Weyl's law.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs P\'olya's conjecture up to $\epsilon$-loss and quantitative estimates for the remainder of Weyl's law
Reference 30
- Resolution
- verified exact
- local_arxiv, observed 2026-07-03T11:28:04.512269Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7596c701-8c4e-45f2-874e-9163d8115160 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 31
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 59703a6b-3ced-46ac-ac45-c26bbfc3fc5a · outbound
This paper cites Kovaˇ r´ ık, S.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Kovaˇ r´ ık, S
Reference 32
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 00b605be-13f6-4941-befc-b17b2d4e33c1 · outbound
This paper cites Leydold, A Faber-Krahn-type inequality for regular trees,Geom.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Leydold, A Faber-Krahn-type inequality for regular trees,Geom
Reference 33
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0adaf3d8-a806-4808-a1a0-af05ef24e21e · outbound
This paper cites Leydold, The geometry of regular trees with the Faber-Krahn property,Discrete Math.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Leydold, The geometry of regular trees with the Faber-Krahn property,Discrete Math
Reference 34
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7ecfa7ec-5181-4f0c-b668-f594938ba97a · outbound
This paper cites Li and S.-T.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Li and S.-T
Reference 35
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 00f48c48-6e6c-4bad-91aa-f00029038cf3 · outbound
This paper cites Li and K.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Li and K
Reference 36
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c26f6216-6ba4-4fdc-8dd3-90fe6ec7eee8 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 37
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T11:28:04.514775Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d13392ba-d7a6-4240-b936-1ff34a90f1ab · outbound
This paper cites Lin and B.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Lin and B
Reference 38
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ba85480f-8672-4d98-8085-02464077dade · outbound
This paper cites Lov´ asz and J.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Lov´ asz and J
Reference 39
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b1103a19-34e4-4521-94d6-a5f2e6a4baf5 · outbound
This paper cites Neumaier, The second largest eigenvalue of a tree,Linear Algebra Appl.46(1982), 9–25.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Neumaier, The second largest eigenvalue of a tree,Linear Algebra Appl.46(1982), 9–25
Reference 40
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cdd64827-261a-427d-804b-149e5a10f6f6 · outbound
This paper cites Gaussian upper heat kernel bounds and Faber-Krahn inequalities on graphs.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Gaussian upper heat kernel bounds and Faber-Krahn inequalities on graphs
Reference 41
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T11:28:04.505387Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7f786eb1-8870-44a7-a370-4e953b77ced9 · outbound
This paper cites Rowlinson, On the maximal index of graphs with a prescribed number of edges,Linear Algebra Appl.110(1988) 43–53.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Rowlinson, On the maximal index of graphs with a prescribed number of edges,Linear Algebra Appl.110(1988) 43–53
Reference 42
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9443b492-668a-407e-9706-fe7081002702 · outbound
This paper cites Nikiforov, Some inequalities for the largest eigenvalue of a graph,Combinatorics, Probability and Computing11(2002),no.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Nikiforov, Some inequalities for the largest eigenvalue of a graph,Combinatorics, Probability and Computing11(2002),no
Reference 43
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b97425da-7a92-4875-b115-d182f12a7749 · outbound
This paper cites P´ olya, On the eigenvalues of vibrating membranes,Proc.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs P´ olya, On the eigenvalues of vibrating membranes,Proc
Reference 44
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e6a86b59-2720-4779-b56e-0c67f6ed81f2 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 45
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 584fad20-2317-49fc-a7a6-f12273fe7688 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 46
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6b5bc853-b008-41f5-8e2c-339f8b6b0605 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 47
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ed128ca6-19a8-4ca8-8498-599af64c38ef · outbound
This paper cites Tait and J.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Tait and J
Reference 48
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6ce783d2-d50b-48d4-9cf1-c5a022f6b18f · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 49
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0ed6a6fb-0f69-41d2-ab8c-5f88be083655 · outbound
This paper cites an unresolved cited work.
Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs Unresolved cited work
Reference 50
- Resolution
- unresolved
- no resolver link, observed 2026-06-27T09:32:43.371239Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
No inbound Pith citation observations are available.