Paper Citation Record · LEDGER

Two Distinct Eigenvalues from a New Graph Product

As of 24 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2501.04297.

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

pith.paper-citation-record.v1
2501.04297 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T21:45:24.984425Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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

13 of 13 outbound references displayed

verified exact1
verified fuzzy12
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ffedd6b4-23a4-4932-8a63-33d75596b798 · outbound

This paper cites Bordering of symmetric matrices an d an application to the minimum number of distinct eigenvalues for the join of graphs.

Two Distinct Eigenvalues from a New Graph Product Bordering of symmetric matrices an d an application to the minimum number of distinct eigenvalues for the join of graphs

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:45:25.139017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b75ceca9-cf1b-4277-9d6a-ffc26cd9cd09 · outbound

This paper cites Achievable multiplicity partitions in the inverse eigenvalue problem of a g raph.

Two Distinct Eigenvalues from a New Graph Product Achievable multiplicity partitions in the inverse eigenvalue problem of a g raph

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:45:25.130734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 1927e356-4309-4917-9c68-f2c317c2a055 · outbound

This paper cites Minimum number of distinct eigenvalues of graphs.

Two Distinct Eigenvalues from a New Graph Product Minimum number of distinct eigenvalues of graphs

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:45:25.121413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 68808d88-55a2-4bd1-ab8b-df5910d26448 · outbound

This paper cites The inverse eigenvalue problem of a gra ph: Multiplicities and minors.

Two Distinct Eigenvalues from a New Graph Product The inverse eigenvalue problem of a gra ph: Multiplicities and minors

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:45:25.112295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 448e0736-29c0-4d35-9418-b3cc45b9bfd4 · outbound

This paper cites Sparsity of graphs that allow tw o distinct eigenvalues.

Two Distinct Eigenvalues from a New Graph Product Sparsity of graphs that allow tw o distinct eigenvalues

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:45:25.103242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b59d9b3c-06a3-4fdd-b916-3bc305d47e7d · outbound

This paper cites Regular graphs of degree at most four that allow two distinct eigenv alues.

Two Distinct Eigenvalues from a New Graph Product Regular graphs of degree at most four that allow two distinct eigenv alues

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:45:25.093397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ed0c0be8-c88d-40bc-bf52-4029baef771f · outbound

This paper cites Graphs with Bipartite Complement that Admit Two Distinct Eigenvalues.

Two Distinct Eigenvalues from a New Graph Product Graphs with Bipartite Complement that Admit Two Distinct Eigenvalues

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-10T21:45:25.017826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2c648632-d4c2-4216-a62f-255ddce8d934 · outbound

This paper cites Generalizations of the strong arnold property and the minimum numb er of distinct eigenvalues of a graph.

Two Distinct Eigenvalues from a New Graph Product Generalizations of the strong arnold property and the minimum numb er of distinct eigenvalues of a graph

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:45:25.082946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation bf001bde-6eea-4a21-b91e-ee18bd333769 · outbound

This paper cites Zero forcing s ets and the minimum rank of graphs.

Two Distinct Eigenvalues from a New Graph Product Zero forcing s ets and the minimum rank of graphs

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:45:25.072001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8f0a1130-3a9f-4735-ba57-fd1fdd809860 · outbound

This paper cites Inverse problems and zero forcing for graphs , volume 270.

Two Distinct Eigenvalues from a New Graph Product Inverse problems and zero forcing for graphs , volume 270

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:45:25.061547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation adc51fb1-0b56-492f-a130-791521696dc8 · outbound

This paper cites On the minimum num ber of distinct eigenvalues for a symmetric matrix whose graph is a given tree.

Two Distinct Eigenvalues from a New Graph Product On the minimum num ber of distinct eigenvalues for a symmetric matrix whose graph is a given tree

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:45:25.051216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation bf0caa1a-aca0-49b6-a0b2-845760d1f6f4 · outbound

This paper cites A nordhaus–gaddum conjecture for the minimum number of distinct eigenvalues of a graph.

Two Distinct Eigenvalues from a New Graph Product A nordhaus–gaddum conjecture for the minimum number of distinct eigenvalues of a graph

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:45:25.039351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ad4f9422-49f9-45d3-a33e-c78d45830028 · outbound

This paper cites Orthogonal symmetric matrices and joins of graphs.

Two Distinct Eigenvalues from a New Graph Product Orthogonal symmetric matrices and joins of graphs

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:45:25.028993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

No inbound Pith citation observations are available.