Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-13T22:43:59.449819Z
Paper Citation Record · LEDGER
Maximum spectral sum of graphs
As of 18 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 3 inbound Pith citation observations for arXiv:2604.00512.
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 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-04T07:42:47.499883Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-05T02:28:24.338817Z
Reference resolution
36 of 36 outbound references displayed
- verified exact0
- verified fuzzy29
- unresolved7
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
0
pith, observed 2026-08-05T02:28:24.338817Z
Outbound references
Observation 9aa9ce97-1ea1-4247-8cb4-72e8022086e6 · outbound
This paper cites A survey of automated conjectures in spectral graph theory.Linear Algebra Appl., 432(9):2293–2322.
Maximum spectral sum of graphs A survey of automated conjectures in spectral graph theory.Linear Algebra Appl., 432(9):2293–2322
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.597093Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 5aa6af60-c30f-415b-88b0-f171da545db9 · outbound
This paper cites A survey of Nordhaus-Gaddum type relations.Discrete Appl.
Maximum spectral sum of graphs A survey of Nordhaus-Gaddum type relations.Discrete Appl
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.600445Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ae81be76-3522-43e5-8b30-40485f880548 · outbound
This paper cites Pure and Applied Mathematics (New York).
Maximum spectral sum of graphs Pure and Applied Mathematics (New York)
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.603950Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e1905b4b-c91c-4f89-81c1-c79011ff8327 · outbound
This paper cites Borgs, J.
Maximum spectral sum of graphs Borgs, J
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.620244Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 5eaedac2-bd70-416d-9d72-636bef44b46f · outbound
This paper cites Cambridge University Press, Cambridge.
Maximum spectral sum of graphs Cambridge University Press, Cambridge
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.590795Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4004aac5-79cb-4837-8258-9aca7c2b3f64 · outbound
This paper cites an unresolved cited work.
Maximum spectral sum of graphs Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-05-13T22:48:24.586694Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 70f26b9c-aeb0-404c-84f1-b980205f1af1 · outbound
This paper cites On a conjecture of V.
Maximum spectral sum of graphs On a conjecture of V
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.583201Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7aa755d4-92b8-471f-ad2d-aa1842b829e9 · outbound
This paper cites Note on the sum of the smallest and largest eigenvalues of a triangle-free graph.
Maximum spectral sum of graphs Note on the sum of the smallest and largest eigenvalues of a triangle-free graph
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.579681Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 04903b4d-d670-4261-8af0-bdfad34758fd · outbound
This paper cites Cvetkovi´ c and P.
Maximum spectral sum of graphs Cvetkovi´ c and P
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.568809Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a854b3a6-ef8e-4955-929b-e2616c8eabdf · outbound
This paper cites The second largest eigenvalue of a graph (a survey).
Maximum spectral sum of graphs The second largest eigenvalue of a graph (a survey)
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.576163Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 212621f4-9a98-43d3-a721-617734a5383e · outbound
This paper cites On the sum of the k largest eigenvalues of graphs and maximal energy of bipartite graphs.Linear Algebra Appl., 569:175–194.
Maximum spectral sum of graphs On the sum of the k largest eigenvalues of graphs and maximal energy of bipartite graphs.Linear Algebra Appl., 569:175–194
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.565082Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 66385fbc-3197-41f9-839d-3fa5ee98c725 · outbound
This paper cites On the sum of two largest eigenvalues of a symmetric matrix.Linear Algebra Appl., 429(11-12):2781–2787.
Maximum spectral sum of graphs On the sum of two largest eigenvalues of a symmetric matrix.Linear Algebra Appl., 429(11-12):2781–2787
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.533167Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d80ec5a7-0160-466f-a348-dbfa8afb44cf · outbound
This paper cites Additive compound matrices and an inequality for eigenvalues of symmetric- stochastic matrices.Czechoslovak Math.
Maximum spectral sum of graphs Additive compound matrices and an inequality for eigenvalues of symmetric- stochastic matrices.Czechoslovak Math
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.485657Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 109df0c7-62e0-4b3d-ad31-923e8d02740d · outbound
This paper cites Convex combi- nation of first and second eigenvalues of trees.
Maximum spectral sum of graphs Convex combi- nation of first and second eigenvalues of trees
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.607368Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e53e3c56-5e6d-4601-adb0-2866ea438cdc · outbound
This paper cites Graph limits and spectral extremal problems for graphs.SIAM J.
Maximum spectral sum of graphs Graph limits and spectral extremal problems for graphs.SIAM J
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.557491Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 46c365e3-0314-4c3e-a532-c78ac6d4ddf9 · outbound
This paper cites American Mathematical Society, Providence, RI.
Maximum spectral sum of graphs American Mathematical Society, Providence, RI
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.541668Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b5c1ca1f-5c6f-4465-9bf0-da1a15c7598c · outbound
This paper cites Limits of dense graph sequences.J.
Maximum spectral sum of graphs Limits of dense graph sequences.J
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.545665Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation bb9d1aba-1c62-4050-8d58-aa05afcb76b7 · outbound
This paper cites Szemer´ edi’s lemma for the analyst.Geom.
Maximum spectral sum of graphs Szemer´ edi’s lemma for the analyst.Geom
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.553792Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation fed42613-79fd-4b83-b137-98c5198e4d7b · outbound
This paper cites Chelsea Publishing Co., New York, third edition.
Maximum spectral sum of graphs Chelsea Publishing Co., New York, third edition
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.572376Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f44738df-859d-4b24-b39e-3a4b58cc1c1f · outbound
This paper cites Springer.
Maximum spectral sum of graphs Springer
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.615624Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 458efb1a-bd95-4cec-a4fc-f005696b6643 · outbound
This paper cites On the sum of k largest eigenvalues of graphs and symmetric matrices.J.
Maximum spectral sum of graphs On the sum of k largest eigenvalues of graphs and symmetric matrices.J
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.525677Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 788a788d-eef3-4df9-a29d-d0160b924202 · outbound
This paper cites Eigenvalues and degree deviation in graphs.Linear Algebra Appl., 414:347– 360.
Maximum spectral sum of graphs Eigenvalues and degree deviation in graphs.Linear Algebra Appl., 414:347– 360
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.550030Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 6e9fd030-5cb1-4b0a-8cb9-1fbb5dc68e23 · outbound
This paper cites Linear combinations of graph eigenvalues.Electron.
Maximum spectral sum of graphs Linear combinations of graph eigenvalues.Electron
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.529385Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 74dad421-8a1f-4e83-8471-d7e8ca6569ee · outbound
This paper cites Eigenvalue problems of Nordhaus-Gaddum type.Discrete Math., 307(6):774– 780.
Maximum spectral sum of graphs Eigenvalue problems of Nordhaus-Gaddum type.Discrete Math., 307(6):774– 780
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.561305Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3e31a58a-27e5-4f62-a63e-bc9a14c28d84 · outbound
This paper cites XXXVIII ofAmerican Mathematical Society Colloquium Publications.
Maximum spectral sum of graphs XXXVIII ofAmerican Mathematical Society Colloquium Publications
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.504887Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f8093ef7-05bf-477f-8101-d6f09e2b1410 · outbound
This paper cites Parrilo and R.R.
Maximum spectral sum of graphs Parrilo and R.R
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.512013Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f295b0a9-c84b-49db-9465-87205e253f42 · outbound
This paper cites Graphs with small spectral gap.Electron.
Maximum spectral sum of graphs Graphs with small spectral gap.Electron
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.515777Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation d2bb7b93-9519-434f-9786-c6139c23c511 · outbound
This paper cites Cambridge University Press, Cambridge.
Maximum spectral sum of graphs Cambridge University Press, Cambridge
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.501056Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 80b2dddf-d5ed-46c4-824f-30722fca105d · outbound
This paper cites Proof of a conjecture of V.
Maximum spectral sum of graphs Proof of a conjecture of V
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-13T22:48:24.497881Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation cc219a91-7802-404b-a308-947bb5c01475 · outbound
This paper cites an unresolved cited work.
Maximum spectral sum of graphs Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-05-13T22:48:24.494496Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation dd02d05f-ae2a-4a24-9b7f-c1fe3344f439 · outbound
This paper cites an unresolved cited work.
Maximum spectral sum of graphs Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-05-13T22:48:24.594006Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 720d23cf-0e22-403f-87db-e110f8962356 · outbound
This paper cites an unresolved cited work.
Maximum spectral sum of graphs Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-05-13T22:48:24.488859Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 2f75a764-6eec-4ff7-8286-6f6f44e801d6 · outbound
This paper cites More precisely, selected entries of Qnum and T num are replaced by nearby rational numbers of bounded denominator, and then assembled into candidate exact matricesQ rat andT rat.
Maximum spectral sum of graphs More precisely, selected entries of Qnum and T num are replaced by nearby rational numbers of bounded denominator, and then assembled into candidate exact matricesQ rat andT rat
Reference 33
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- raw_fallback, observed 2026-05-13T22:48:24.508705Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 657b8b96-5086-449b-afb3-9c3c66388e89 · outbound
This paper cites an unresolved cited work.
Maximum spectral sum of graphs Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-05-13T22:48:24.520492Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 8408d199-0e79-4f3d-b2b1-b8df835bcf82 · outbound
This paper cites an unresolved cited work.
Maximum spectral sum of graphs Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-05-13T22:48:24.491804Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation ae6c0342-7fe2-490c-8f97-c3b5ee163462 · outbound
This paper cites an unresolved cited work.
Maximum spectral sum of graphs Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-05-13T22:48:24.536965Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Pith citing papers
Observation d98ddbcd-2e6e-4de9-a992-c93ae0681d81 · inbound
Generalized Nordhaus--Gaddum Inequalities for Eigenvalues cites this paper.
Generalized Nordhaus--Gaddum Inequalities for Eigenvalues Maximum spectral sum of graphs
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T22:08:15.120513Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0f3fbad7-915f-48c7-b515-1f29f4bbd106 · inbound
The Exact Maximum of the Spectral Sum of Graphs cites this paper.
The Exact Maximum of the Spectral Sum of Graphs Maximum spectral sum of graphs
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:14:47.923742Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 553545d4-ddb4-47d2-b309-f2db5f5b8390 · inbound
Graph Eigenvalues and Projection Constants cites this paper.
Graph Eigenvalues and Projection Constants Maximum spectral sum of graphs
Reference 11
- Resolution
- verified exact
- local_arxiv, observed 2026-08-04T07:43:20.187629Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.