Paper Citation Record · LEDGER

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family

As of 8 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2507.16169.

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

pith.paper-citation-record.v1
2507.16169 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:29:45.963643Z

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

12 of 12 outbound references displayed

verified exact8
verified fuzzy1
unresolved2
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0850c079-853a-469c-9b88-908c48afdfb9 · outbound

This paper cites Pelayo, Mar\' a L.

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family Pelayo, Mar\' a L

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T15:29:44.856577Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 56a51095-8734-4af6-988f-32d536610712 · outbound

This paper cites Metric D imension of a D irect P roduct of T hree C omplete G raphs.

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family Metric D imension of a D irect P roduct of T hree C omplete G raphs

Reference 2

Resolution: malformed identifier; doi_truncated, observed 2026-08-06T15:29:47.256083Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9171952a-7d5b-437a-a73a-f01ccdcbeb52 · outbound

This paper cites On the Metric Dimension of $K_a \times K_b \times K_c$.

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family On the Metric Dimension of $K_a \times K_b \times K_c$

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:29:47.910170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ad161bc6-3d2c-4fc7-b254-1155ae93d862 · outbound

This paper cites The metric dimension of Z _n Z _n Z _n is 3n/2.

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family The metric dimension of Z _n Z _n Z _n is 3n/2

Reference 4

Resolution: verified exact; doi, observed 2026-08-06T15:29:47.060049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 83f5eb82-b599-4fac-9e80-2e3c29034f4b · outbound

This paper cites New Optimal Results on Codes for Location in Graphs.

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family New Optimal Results on Codes for Location in Graphs

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:29:47.721786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1331f19c-091e-4bd5-960f-2fe2d7d67e1f · outbound

This paper cites The metric dimension of the lexicographic product of graphs.

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family The metric dimension of the lexicographic product of graphs

Reference 6

Resolution: verified exact; doi, observed 2026-08-06T15:29:46.858420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c4c55805-2b2e-4bd5-b8e1-492bb1a96b20 · outbound

This paper cites an unresolved cited work.

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family Unresolved cited work

Reference 7

Resolution: verified exact; doi, observed 2026-08-06T15:29:46.678426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ade16726-6d73-4313-8d7e-fe827f38125e · outbound

This paper cites Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results.

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T15:29:45.566840Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c49ede99-0e3b-456c-ae01-6afbc73b8db5 · outbound

This paper cites Eigenspaces of H amming graphs and unitary C ayley graphs.

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family Eigenspaces of H amming graphs and unitary C ayley graphs

Reference 9

Resolution: verified exact; doi, observed 2026-08-06T15:29:46.477028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3dcdca91-d3c4-4d36-8f7d-adf6cb5c9542 · outbound

This paper cites Tillquist, Rafael M.

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family Tillquist, Rafael M

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:29:48.117988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 005ee99d-cc03-4766-847c-94b767227283 · outbound

This paper cites S ageMath, the S age M athematics S oftware S ystem ( V ersion 10.6) , 2022.

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family S ageMath, the S age M athematics S oftware S ystem ( V ersion 10.6) , 2022

Reference 11

Resolution: verified exact; doi, observed 2026-08-06T15:29:46.250195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c854ff58-add8-4eb4-97f4-178888620ccc · outbound

This paper cites Computing the metric dimension of the categorial product of some graphs.

Metric Dimension of a Direct Product of Three Complete Graphs: The Middle Cone Family Computing the metric dimension of the categorial product of some graphs

Reference 12

Resolution: verified exact; raw_fallback, observed 2026-08-06T15:29:47.503660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

No inbound Pith citation observations are available.