Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T12:04:39.766205Z
Paper Citation Record · LEDGER
Girth and Laplacian eigenvalue distribution
As of 7 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2506.00921.
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 2026-08-07T06:34:17.273281+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
34 of 34 outbound references displayed
- verified exact1
- verified fuzzy21
- unresolved12
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 03ada2db-3090-46ce-9d29-5282a4b9ba3f · outbound
This paper cites Ahanjideh, S.
Girth and Laplacian eigenvalue distribution Ahanjideh, S
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:41.762693Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f53e0c6e-54f4-419b-81ad-bc08f4b09018 · outbound
This paper cites Akbari, M.
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:41.705807Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 18535021-8cd7-47f4-b4a8-2cef843249ad · outbound
This paper cites Anderson, T.D.
Girth and Laplacian eigenvalue distribution Anderson, T.D
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:41.659621Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 8889abee-7c82-4d3d-840c-453b6552a9cc · outbound
This paper cites Braga, V.M.
Girth and Laplacian eigenvalue distribution Braga, V.M
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:41.605497Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4b51db4c-02b9-4f58-bfd3-88f7808eb314 · outbound
This paper cites Brouwer, W.
Girth and Laplacian eigenvalue distribution Brouwer, W
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T12:04:38.888190Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c42c019c-3472-483f-9794-dfbea1140e49 · outbound
This paper cites Cardoso, D.P.
Girth and Laplacian eigenvalue distribution Cardoso, D.P
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:41.524899Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation b07a6ebb-36c9-4a8b-9544-0e9ad83e86ad · outbound
This paper cites an unresolved cited work.
Girth and Laplacian eigenvalue distribution Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:04:41.422209Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 2a49a422-b6ca-494e-977e-07d48a7b3000 · outbound
This paper cites an unresolved cited work.
Girth and Laplacian eigenvalue distribution Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:04:41.360648Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e27ba5c6-1507-4407-a9c8-4d744f788f0b · outbound
This paper cites Das, The largest two Laplacian eigenvalues of a graph, Linear Multilinear Algebra 52(2004) 441–460.
Girth and Laplacian eigenvalue distribution Das, The largest two Laplacian eigenvalues of a graph, Linear Multilinear Algebra 52(2004) 441–460
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:41.298070Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 390dcd65-e118-4c68-a004-b8c90ede2f39 · outbound
This paper cites Faria, Permanental roots and the star degree of a graph, Linear Algebra Appl.
Girth and Laplacian eigenvalue distribution Faria, Permanental roots and the star degree of a graph, Linear Algebra Appl
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:41.231365Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f1b3c347-9a10-4c44-84d2-75addec8f476 · outbound
This paper cites Fiedler, Algebraic connectivity of graphs, Czech.
Girth and Laplacian eigenvalue distribution Fiedler, Algebraic connectivity of graphs, Czech
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:41.171163Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation a69451ba-ea9e-4f77-b314-f9e204468c72 · outbound
This paper cites Goldberg, G.
Girth and Laplacian eigenvalue distribution Goldberg, G
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:41.110309Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 5b5425a9-106e-40be-85eb-a367872a4480 · outbound
This paper cites Grone, R.
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:41.052502Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation b0d74e3a-dbd3-496a-b954-78c911a96149 · outbound
This paper cites Guo, On the second largest Laplacian eigenvalue of trees, Linear Algebra Appl.
Girth and Laplacian eigenvalue distribution Guo, On the second largest Laplacian eigenvalue of trees, Linear Algebra Appl
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:40.991280Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f4f490ce-8b32-4bea-8223-dd8216871967 · outbound
This paper cites an unresolved cited work.
Girth and Laplacian eigenvalue distribution Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:04:40.921778Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4e63b8da-1acd-4502-9388-9fd4aacf2b25 · outbound
This paper cites an unresolved cited work.
Girth and Laplacian eigenvalue distribution Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:04:40.856321Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation b6d402bb-586c-454d-886a-fb0c15f54ce6 · outbound
This paper cites an unresolved cited work.
Girth and Laplacian eigenvalue distribution Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:04:40.777178Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 8253c097-3864-4bf4-9afd-529423cabb37 · outbound
This paper cites Hedetniemi, D.P.
Girth and Laplacian eigenvalue distribution Hedetniemi, D.P
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:40.714157Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f36cefda-b6dd-4012-b080-e4aaa409c8dd · outbound
This paper cites Horn, C.R.
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:40.646730Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0b05d2a6-b492-438a-a982-7f460350f692 · outbound
This paper cites Jacobs, E.R.
Girth and Laplacian eigenvalue distribution Jacobs, E.R
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:40.585754Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation bd40873a-ed68-44ca-ba09-c7f53173313b · outbound
This paper cites Kirkland, J.J.
Girth and Laplacian eigenvalue distribution Kirkland, J.J
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:40.535593Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e3a8a11c-ba6a-4f94-8d4e-a7d8900fc92a · outbound
This paper cites Merris, Laplacian matrices of graphs: a survey, Linear Algebra Appl.
Girth and Laplacian eigenvalue distribution Merris, Laplacian matrices of graphs: a survey, Linear Algebra Appl
Reference 22
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T12:04:39.473425Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 17be4c66-2a0a-4380-831a-7cb4adadf1a8 · outbound
This paper cites Merris, The number of eigenvalues greater than two in the Laplacian spectrum of a graph, Portugal.
Girth and Laplacian eigenvalue distribution Merris, The number of eigenvalues greater than two in the Laplacian spectrum of a graph, Portugal
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:40.453097Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 50e71407-b66d-4ea8-9d8c-30379a723941 · outbound
This paper cites Mohar, The Laplacian spectrum of graphs, in: Y.
Girth and Laplacian eigenvalue distribution Mohar, The Laplacian spectrum of graphs, in: Y
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:40.382345Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 651658eb-1ed3-42ef-965b-ebf7d6183834 · outbound
This paper cites Mohar, Laplace eigenvalues of graphs–a survey, Discrete Math.
Girth and Laplacian eigenvalue distribution Mohar, Laplace eigenvalues of graphs–a survey, Discrete Math
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:40.323856Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation b35ac3b7-8091-4077-b04f-b081ef5d7950 · outbound
This paper cites Pan, Sharp upper bounds for the Laplacian graph eigenvalues, Linear Algebra Appl.
Girth and Laplacian eigenvalue distribution Pan, Sharp upper bounds for the Laplacian graph eigenvalues, Linear Algebra Appl
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:40.259094Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 022e5b56-c2ae-4811-8bf2-4393602218a7 · outbound
This paper cites Sin, On the number of Laplacian eigenvalues of trees less than the average degree, Discrete Math.
Girth and Laplacian eigenvalue distribution Sin, On the number of Laplacian eigenvalues of trees less than the average degree, Discrete Math
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:40.198507Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 2d88a9c2-e3aa-44c7-877f-4c55d423dbbf · outbound
This paper cites So, Commutativity and spectra of Hermitian matrices, Linear Algebra Appl.
Girth and Laplacian eigenvalue distribution So, Commutativity and spectra of Hermitian matrices, Linear Algebra Appl
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T12:04:40.151589Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e6bb0e59-a171-4809-b5a5-82659417a592 · outbound
This paper cites an unresolved cited work.
Girth and Laplacian eigenvalue distribution Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:04:40.099637Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 67812df3-e873-4558-b436-1364e6bb6120 · outbound
This paper cites an unresolved cited work.
Girth and Laplacian eigenvalue distribution Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:04:40.039348Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation bdd334a9-07e2-42ee-8bda-5edb90ea16d3 · outbound
This paper cites an unresolved cited work.
Girth and Laplacian eigenvalue distribution Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:04:39.986211Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 04385875-b97c-486c-b104-102804df5191 · outbound
This paper cites The Laplacian eigenvalues of graphs: a survey.
Girth and Laplacian eigenvalue distribution The Laplacian eigenvalues of graphs: a survey
Reference 32
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T12:04:39.733949Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0a8a50d8-3390-4b1f-b6fb-087953b46669 · outbound
This paper cites Laplacian eigenvalue distribution and girth of graphs.
Girth and Laplacian eigenvalue distribution Laplacian eigenvalue distribution and girth of graphs
Reference 33
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T12:04:39.843096Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 95147e01-cb34-4224-b249-320d06bbd451 · outbound
This paper cites an unresolved cited work.
Girth and Laplacian eigenvalue distribution Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T12:04:39.929717Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Pith citing papers
No inbound Pith citation observations are available.