Paper Citation Record · LEDGER

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications

As of 10 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 1 inbound Pith citation observation for arXiv:2605.26707.

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

pith.paper-citation-record.v1
2605.26707 v2

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-29T17:41:13.667818Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T04:14:47.950006Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

22 of 22 outbound references displayed

verified exact2
verified fuzzy0
unresolved20
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9b36deb6-d984-4f8a-a641-6474fce9761e · outbound

This paper cites Ashraf, G.R.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Ashraf, G.R

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7e1e3a68-7da3-4c59-999e-3b2a78b2b317 · outbound

This paper cites an unresolved cited work.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe70dc67-afd5-4892-a863-f912b9c6abd7 · outbound

This paper cites an unresolved cited work.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d235559-5b68-48ba-8440-5d075efd3a3a · outbound

This paper cites de Caen, An upper bound on the sum of squares of degrees in a graph,Discrete Math.185(1–3) (1998) 245–248.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications de Caen, An upper bound on the sum of squares of degrees in a graph,Discrete Math.185(1–3) (1998) 245–248

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b5fbbf2c-2de9-4a11-9b1a-1ab7e3fb95ac · 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.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Chen, On Brouwer’s conjecture for the sum of k largest Laplacian eigenvalues of graphs,Linear Algebra Appl.578(2019) 402–410

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16cbead0-047e-4d04-bc0e-e37b0a82f818 · outbound

This paper cites More on the full Brouwer Laplacian spectrum conjecture.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications More on the full Brouwer Laplacian spectrum conjecture

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-06-29T17:53:47.842156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1403aa81-1da7-4c6e-b504-c3447237d3e9 · outbound

This paper cites Cvetkovic, M.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Cvetkovic, M

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation defac70c-1c2f-4697-80ec-4ebb4b25e7ab · outbound

This paper cites Collatz, U.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Collatz, U

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6c9c89e-903b-4f1a-a955-c600e02c6701 · outbound

This paper cites an unresolved cited work.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1ee8534d-b143-45ee-81d4-ca46fd40735e · outbound

This paper cites an unresolved cited work.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 49916b0a-1522-496e-8c44-f51a4640ecbe · outbound

This paper cites an unresolved cited work.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86b3dcaf-4334-41b6-8792-84c3198915b1 · outbound

This paper cites an unresolved cited work.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5367835c-cf75-42c1-8adb-c0a82f528f49 · outbound

This paper cites an unresolved cited work.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Unresolved cited work

Reference 13

Resolution: verified exact; doi, observed 2026-06-29T17:43:45.040361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1b1d34c8-b5e4-4317-81cd-fc3e3ef1c35d · outbound

This paper cites an unresolved cited work.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 49aaee41-ea28-421c-96a6-1811df306e12 · outbound

This paper cites an unresolved cited work.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8a1c357-af64-4d2a-95f9-6e7f6af2389c · outbound

This paper cites Merris, Laplacian matrices of graphs: A survey,Linear Algebra Appl.197, 198 (1994) 143–176.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Merris, Laplacian matrices of graphs: A survey,Linear Algebra Appl.197, 198 (1994) 143–176

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dcad4603-92d2-47b7-8c31-f34646db25f0 · outbound

This paper cites Mohar, On the sum of k largest eigenvalues of graphs and symmetric matrices,J.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Mohar, On the sum of k largest eigenvalues of graphs and symmetric matrices,J

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9631eb2-b69d-427e-a369-9bfb87fac66b · outbound

This paper cites Nikiforov, Linear combinations of graph eigenvalues,Electron.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Nikiforov, Linear combinations of graph eigenvalues,Electron

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30b2dbc6-743b-40c6-a5f7-c25bb50174c6 · outbound

This paper cites Nikiforov, Beyond graph energy: norms of graphs and matrices,Linear Algebra Appl.506(2016) 82–138.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Nikiforov, Beyond graph energy: norms of graphs and matrices,Linear Algebra Appl.506(2016) 82–138

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf23abd3-582e-4de4-b992-8175daf8120f · outbound

This paper cites an unresolved cited work.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0300d702-4ea9-4bb7-8b71-72735c7af0fd · outbound

This paper cites an unresolved cited work.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation acb4e3ea-4168-4b12-a71e-79945ccc3b7b · outbound

This paper cites Zhang, H.

Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications Zhang, H

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-29T17:41:13.667818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 5a480db6-abaa-410b-86f4-bb33b2d76303 · inbound

The Exact Maximum of the Spectral Sum of Graphs cites this paper.

The Exact Maximum of the Spectral Sum of Graphs Sum of the $k$ Largest Eigenvalues of Symmetric Matrices: Theory and Applications

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T04:14:47.950006Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.