Paper Citation Record · LEDGER

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions

As of 21 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 1 inbound Pith citation observation for arXiv:2606.06774.

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

pith.paper-citation-record.v1
2606.06774 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-28T00:06:57.716557Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-02T03:44:12.780508Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-02T03:46:32.075038Z

Reference resolution

26 of 26 outbound references displayed

verified exact2
verified fuzzy0
unresolved24
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 961ec3bf-92ab-4b3c-ae60-b11814df306e · outbound

This paper cites Imprimitivity index of the adjacency matrix of digraphs.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Imprimitivity index of the adjacency matrix of digraphs

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a627aa9a-a6da-44d6-a814-baa061e078fe · outbound

This paper cites On the unitary Cayley graph of a finite ring.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions On the unitary Cayley graph of a finite ring

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

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Observation 34d00519-99dc-4bce-957e-09bdec100d80 · outbound

This paper cites On restricted unitary Cayley graphs and symplectic transformations modulo n.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions On restricted unitary Cayley graphs and symplectic transformations modulo n

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

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Observation 67a71689-5cec-4f2f-9365-a7078240c321 · outbound

This paper cites Spectra of digraphs.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Spectra of digraphs

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 761fe033-7fb2-449b-b58a-11bf12d4fbf9 · outbound

This paper cites an unresolved cited work.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

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Observation 1d39ffab-c670-4f93-809e-024e89e6a0da · outbound

This paper cites Matrix Analysis.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Matrix Analysis

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

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Observation 440f9f7f-87be-4817-b00e-61476d2a181d · outbound

This paper cites Graph theory.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Graph theory

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

Source-reported events for the cited work

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Observation 61e447f2-90b1-464e-9cc0-f044cd61488f · outbound

This paper cites The energy of unitary Cayley graphs.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions The energy of unitary Cayley graphs

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 43403656-9a09-4b9d-9813-1380745b3d92 · outbound

This paper cites Characterisations and Galois conjugacy of generalised Paley maps.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Characterisations and Galois conjugacy of generalised Paley maps

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

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Unavailable: canonical work link unavailable.

Observation 8f3ed0a6-b2a9-46af-b5c4-f2db908ecdd7 · outbound

This paper cites Dessins d'Enfants on Riemann Surfaces.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Dessins d'Enfants on Riemann Surfaces

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

Source-reported events for the cited work

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Observation be528302-fd1c-4825-aa4e-eec0c18f4716 · outbound

This paper cites Energy of unitary Cayley graphs and gcd-graphs.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Energy of unitary Cayley graphs and gcd-graphs

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation afdf647c-538d-48e3-8c9f-22377de501ef · outbound

This paper cites On generalised Paley graphs and their automorphism groups.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions On generalised Paley graphs and their automorphism groups

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d7d919eb-32ab-4b20-87c0-95961fc4adf9 · outbound

This paper cites Spectral properties of unitary Cayley graphs of finite commutative rings.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Spectral properties of unitary Cayley graphs of finite commutative rings

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3cf54a8a-feb5-41ea-993a-35e527f1dc10 · outbound

This paper cites Quadratic unitary cayley graphs of finite commutative rings.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Quadratic unitary cayley graphs of finite commutative rings

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

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Observation 7317b0c0-79fb-46f6-aed7-20daefbd1223 · outbound

This paper cites On certain properties of the $p$-unitary Cayley graph over a finite ring.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions On certain properties of the $p$-unitary Cayley graph over a finite ring

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-07-02T14:57:04.339170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0ac90ff1-329f-4c1b-8a5a-ffe401d15627 · outbound

This paper cites Generalised Paley graphs with a product structure.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Generalised Paley graphs with a product structure

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

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Observation 1543a97c-e88a-4333-b38d-3ddcaef1f6ea · outbound

This paper cites Integral equienergetic non-isospectral unitary Cayley graphs, Linear Algebra Appl.\@ 612, (2021) 42--74.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Integral equienergetic non-isospectral unitary Cayley graphs, Linear Algebra Appl.\@ 612, (2021) 42--74

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

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Observation ab23cd09-dc81-438c-8e8c-dc3a544cbb5d · outbound

This paper cites A reduction formula for Waring numbers through generalized Paley graphs.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions A reduction formula for Waring numbers through generalized Paley graphs

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

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Observation fdffc189-0958-45d6-a10b-f834f6f5a317 · outbound

This paper cites The weight distribution of irreducible cyclic codes associated with decomposable generalized Paley graphs.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions The weight distribution of irreducible cyclic codes associated with decomposable generalized Paley graphs

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

Source-reported events for the cited work

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Observation eb6be112-9665-4606-bb85-714a911071a7 · outbound

This paper cites Waring numbers over finite commutative local rings.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Waring numbers over finite commutative local rings

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

Source-reported events for the cited work

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Observation e72e3b8f-2f5e-4eac-88a9-888f8e4b5822 · outbound

This paper cites Generalized Paley graphs equienergetic with their complements.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Generalized Paley graphs equienergetic with their complements

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d9358133-4e5c-40e7-a904-3a66a82cafd3 · outbound

This paper cites Spectral properties of generalized Paley graphs.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Spectral properties of generalized Paley graphs

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b073b4c5-1807-48a3-8a0e-1d352080ba22 · outbound

This paper cites Connected components and non-bipartiteness of generalized Paley graphs.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions Connected components and non-bipartiteness of generalized Paley graphs

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

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Observation 8b7f8c84-2c63-40d6-b71a-5fafd2037b13 · outbound

This paper cites The nature of the spectrum of generalized Paley graphs and weak Waring numbers over finite fields.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions The nature of the spectrum of generalized Paley graphs and weak Waring numbers over finite fields

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-06-28T02:01:29.762382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8e6933bf-0002-41c1-95c2-8bc193a84349 · outbound

This paper cites On diagonal equations over finite fields via walks in NEPS of graphs.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions On diagonal equations over finite fields via walks in NEPS of graphs

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

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Observation e39311bb-400c-447e-bf75-e4a7c21770fb · outbound

This paper cites The Kronecker product of graphs.

On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions The Kronecker product of graphs

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-28T00:06:57.716557Z

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Pith citing papers

Observation dd666f40-f36d-4919-a01e-32238aaed1c0 · inbound

Sums of units in finite rings and applications to Cayley graphs cites this paper.

Sums of units in finite rings and applications to Cayley graphs On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions

Reference 37

Resolution: verified exact; local_arxiv, observed 2026-07-02T03:46:32.077364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.