Paper Citation Record · LEDGER

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues

As of 15 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2607.17293.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2607.17293 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T18:35:01.255087Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

28 of 28 outbound references displayed

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unresolved28
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External citation measurements

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Outbound references

Observation a396bb5f-d847-46bc-af9f-a260d930ce3b · outbound

This paper cites Bai,The Grone–Merris conjecture, Trans.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Bai,The Grone–Merris conjecture, Trans

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T18:34:59.628428Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a090a605-f148-4acf-924d-78e707eca5b7 · outbound

This paper cites Berndsen,Three problems in algebraic combinatorics, Master’s thesis, Eindhoven University of Technology, 2012.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Berndsen,Three problems in algebraic combinatorics, Master’s thesis, Eindhoven University of Technology, 2012

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T18:34:59.678159Z

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Observation 4a2938ac-6828-4b8d-a16a-290292f0ce16 · outbound

This paper cites an unresolved cited work.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T18:34:59.724878Z

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Unavailable: canonical work link unavailable.

Observation 76a7301b-51c9-4a5c-b89e-0777b09848a0 · outbound

This paper cites The Equality Cases For the Laplacian Conjecture of Brouwer.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues The Equality Cases For the Laplacian Conjecture of Brouwer

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T18:34:59.778446Z

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Unavailable: canonical work link unavailable.

Observation 422992aa-9f7c-4e0b-880b-1307ac9d0d0c · outbound

This paper cites Chen,Improved results on Brouwer’s conjecture for sum of the Laplacian eigenvalues of a graph, Linear Algebra Appl.557(2018), 327–338.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Chen,Improved results on Brouwer’s conjecture for sum of the Laplacian eigenvalues of a graph, Linear Algebra Appl.557(2018), 327–338

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T18:34:59.870579Z

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Observation b5de856e-bfdb-4e5c-8e32-0e157fa60cbb · outbound

This paper cites Chen,On Brouwer’s conjecture for the sum of k largest Laplacian eigenvalues of graphs, Linear Algebra Appl.578(2019), 402–410.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Chen,On Brouwer’s conjecture for the sum of k largest Laplacian eigenvalues of graphs, Linear Algebra Appl.578(2019), 402–410

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T18:34:59.934750Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22103560-d324-459a-94ce-13a22da59022 · outbound

This paper cites Chen and J.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Chen and J

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.005332Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 71e53648-e724-44e5-812c-dc7e38a60faa · outbound

This paper cites an unresolved cited work.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.093113Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac7e07db-2462-4ec8-bda3-7d01140e5ecd · outbound

This paper cites Du and B.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Du and B

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.164983Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c4ed3b70-ad0b-4656-a0de-02950de5db7c · outbound

This paper cites an unresolved cited work.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.220838Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 228ba760-adb5-4073-bd6f-763914193fb0 · outbound

This paper cites an unresolved cited work.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.279627Z

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Observation 171daf3a-f395-4e94-9a72-5e9a6a47ee7e · outbound

This paper cites Grone and R.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Grone and R

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.330654Z

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Observation 9ab2f9fc-32ec-42e2-852a-cfbcc8e5bd4a · outbound

This paper cites an unresolved cited work.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.374506Z

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Observation 8dd58c3d-c8a9-48bd-b9b9-bd4274e7bf9a · outbound

This paper cites Helmberg and V.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Helmberg and V

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.457080Z

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Unavailable: canonical work link unavailable.

Observation b8011a08-6c1c-4063-a1f2-73fde2170914 · outbound

This paper cites On Brouwer's Laplacian conjecture.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues On Brouwer's Laplacian conjecture

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.526082Z

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Observation 7559af5b-0031-419a-93e2-d8d9d2e0e395 · outbound

This paper cites Kumar, S.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Kumar, S

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.608944Z

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Unavailable: canonical work link unavailable.

Observation a0276e5b-d1dc-4514-9fef-f309a48ce2d8 · outbound

This paper cites Lew,Partition density, star arboricity, and sums of laplacian eigenvalues of graphs, J.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Lew,Partition density, star arboricity, and sums of laplacian eigenvalues of graphs, J

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.662289Z

Source-reported events for the cited work

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Observation e61bf069-fc4a-436a-a297-dbdeefd4a6af · outbound

This paper cites Sums of Laplacian eigenvalues and sums of degrees.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Sums of Laplacian eigenvalues and sums of degrees

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.733449Z

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Observation dd4eb52b-6a63-4fc5-8c31-9ab48cfdc491 · outbound

This paper cites Lew,An approximate version of Brouwer’s Laplacian conjecture, arXiv:2601.17575, 2026.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Lew,An approximate version of Brouwer’s Laplacian conjecture, arXiv:2601.17575, 2026

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.806522Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72495278-c9fb-4382-8ccc-1b0facb8f82d · outbound

This paper cites Li and J.-M.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Li and J.-M

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.861037Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0a780805-ce57-4afd-addd-a7f7ff17fb0b · outbound

This paper cites an unresolved cited work.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.918696Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d7deb633-ce1e-4f29-8132-e72884376922 · outbound

This paper cites an unresolved cited work.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:00.983897Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eec45ce8-d1dc-4219-9811-ce5b8760148b · outbound

This paper cites Rocha and V.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Rocha and V

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:01.040419Z

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Observation 57eaf493-86c7-4c2a-b04f-3fcea6542bfa · outbound

This paper cites Rocha,Brouwer’s conjecture holds asymptotically almost surely, Linear Algebra Appl.597 (2020), 198–205.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Rocha,Brouwer’s conjecture holds asymptotically almost surely, Linear Algebra Appl.597 (2020), 198–205

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:01.091873Z

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Unavailable: canonical work link unavailable.

Observation d154e087-1a44-4147-99e4-9ae5defd8f5d · outbound

This paper cites an unresolved cited work.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:01.183858Z

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Unavailable: canonical work link unavailable.

Observation 71a839e5-009c-47df-8692-27f93caff061 · outbound

This paper cites an unresolved cited work.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:01.235367Z

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Unavailable: canonical work link unavailable.

Observation b4801dd6-6dfb-4748-971c-6cea800517ae · outbound

This paper cites an unresolved cited work.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:01.240190Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eec27e28-ae72-4b4a-a553-5acba49ee188 · outbound

This paper cites an unresolved cited work.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T18:35:01.255087Z

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Pith citing papers

No inbound Pith citation observations are available.