Paper Citation Record · LEDGER

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture

As of 16 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2607.08452.

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

pith.paper-citation-record.v1
2607.08452 v2

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-14T15:33:15.240468Z

measured 23 of 23 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.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

23 of 23 outbound references displayed

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Outbound references

Observation 4ef0f896-a31d-46c5-8ee7-f9323b4d4266 · outbound

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

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Bai, The Grone–Merris conjecture,Trans

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee0bab24-a14e-4509-b774-28ca7b90142e · outbound

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

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Berndsen, Three problems in algebraic combinatorics,Master’s thesis, Eindhoven University of Technology, 2012

Reference 2

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Observation fb96a3c3-4324-4503-9939-04054963fefc · outbound

This paper cites Brouwer, W.H.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Brouwer, W.H

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 4f852a1d-ba77-49ab-b28e-e6ed9e65af1f · outbound

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

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture The Equality Cases For the Laplacian Conjecture of Brouwer

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 97219b54-0bfc-469c-9341-127bfafee794 · 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.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture 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 2026-07-14T15:33:15.240468Z

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Observation 5463a604-ff5e-414c-877b-82d949f76995 · outbound

This paper cites Chen, On Brouwer’s conjecture for the sum ofklargest Laplacian eigen- values of graphs,Linear Algebra Appl.578(2019), 402–410.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Chen, On Brouwer’s conjecture for the sum ofklargest Laplacian eigen- values of graphs,Linear Algebra Appl.578(2019), 402–410

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 19d580ea-6557-4094-b810-bdddf6223b4a · outbound

This paper cites Cooper, Constraints on Brouwer’s Laplacian spectrum conjecture,Lin- ear Algebra Appl.615(2021), 11–27.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Cooper, Constraints on Brouwer’s Laplacian spectrum conjecture,Lin- ear Algebra Appl.615(2021), 11–27

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 20d265b6-31bb-4beb-9f33-b6f7cb202f56 · outbound

This paper cites Das, S.A.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Das, S.A

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation fad82311-3e3f-40b5-a104-5aa12ef4c9ac · outbound

This paper cites an unresolved cited work.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 58bbbf9c-a0e0-4721-a1bd-54a21eb2b3e0 · outbound

This paper cites Edmonds, Paths, trees, and flowers,Canad.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Edmonds, Paths, trees, and flowers,Canad

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 6a9430ae-7d51-4698-b409-1ca316721ae4 · outbound

This paper cites Ganie, S.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Ganie, S

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 955aeac2-c450-4091-a7c0-aff772b7f03a · outbound

This paper cites Grone, R.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Grone, R

Reference 12

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Observation fdfc0b1e-85d4-4bba-bdf7-53d5b99c952e · outbound

This paper cites Haemers, A.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Haemers, A

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 96c6b01a-2ea7-4d62-bda0-651659400647 · outbound

This paper cites A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality

Reference 14

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Observation cec2dc71-ad6f-4f2a-ba8e-f12fb7c706b9 · outbound

This paper cites On Brouwer's Laplacian conjecture.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture On Brouwer's Laplacian conjecture

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 0c01024e-4cfe-4182-89e7-2704c11046c1 · outbound

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

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Lew, Partition density, star arboricity, and sums of Laplacian eigenvalues of graphs,J

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 04d70e58-f487-48f2-aa39-c299867a98a1 · outbound

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

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Sums of Laplacian eigenvalues and sums of degrees

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation d66e6894-2a52-45d3-8f6d-c66e36592509 · outbound

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

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Lew, An approximate version of Brouwer’s Laplacian conjecture, arXiv:2601.17575, 2026

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 7889b6f6-a2f8-47a3-8e77-29f190f429ca · outbound

This paper cites an unresolved cited work.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation e93d2568-c453-433a-bbcb-133468d37d1c · outbound

This paper cites an unresolved cited work.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation e152297a-657f-463d-af65-e671c77dfd26 · outbound

This paper cites an unresolved cited work.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 15333993-fb45-4457-a2a0-0d25af0897bc · outbound

This paper cites Torres, V.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Torres, V

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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Observation 1beb1e9f-e5c1-4c80-ba23-0ae9e59f8d38 · outbound

This paper cites an unresolved cited work.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-14T15:33:15.240468Z

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