Pith Number

pith:7FF4376N

pith:2026:7FF4376NQKILC6WRLEYYXWZQGT

not attested not anchored not stored refs resolved

A Study on Type-2 Isomorphic Circulant Graphs: Part 8: $C_{432}(R)$, $C_{6750}(S)$ -- each has 2 types of Type-2 isomorphic circulant graphs

Vilfred Kamalappan

Families of circulant graphs C_432(R) each admit Type-2 isomorphisms for both m=2 and m=3, and families C_6750(S) do so for both m=3 and m=5.

arxiv:2605.14402 v1 · 2026-05-14 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7FF4376NQKILC6WRLEYYXWZQGT}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Family of circulant graphs C_432(R), each has isomorphic circulant graphs of Type-2 w.r.t. m = 2 as well as m = 3; and Family of circulant graphs C_6750(S), each has isomorphic circulant graphs of Type-2 w.r.t. m = 3 as well as m = 5.

C2weakest assumption

The specific connection sets R and S are assumed to produce the claimed Type-2 isomorphisms under the definitions established in the author's prior seven papers; this assumption is not independently verified or derived in the abstract.

C3one line summary

Two families of circulant graphs C_432(R) and C_6750(S) each possess Type-2 isomorphic variants for two values of m.

References

21 extracted · 21 resolved · 1 Pith anchors

[1] A. Adam,Research problem 2-10, J. Combinatorial Theory,3(1967), 393 1967

[2] J. A. Bondy and U. S. R. Murty,Graph Theory with Applications,5 th Edi., Elsevier Sci. Publ. Co., New York, 1982 1982

[3] P. J. Davis,Circulant Matrices,Wiley, New York, 1979 1979

[4] West,Introduction to Graph Theory,2 ed Edi., Pearson Education (Singapore) Pvt 2002

[5] B. Elspas and J. Turner,Graphs with circulant adjacency matrices, J. Combinatorial Theory,9(1970), 297-307 1970

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:07.470464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f94bcdffcd8290b17ad159318bdb3034cb97953b98f11d5aae0ed9c9e24da1b9

Aliases

arxiv: 2605.14402 · arxiv_version: 2605.14402v1 · doi: 10.48550/arxiv.2605.14402 · pith_short_12: 7FF4376NQKIL · pith_short_16: 7FF4376NQKILC6WR · pith_short_8: 7FF4376N

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7FF4376NQKILC6WRLEYYXWZQGT \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f94bcdffcd8290b17ad159318bdb3034cb97953b98f11d5aae0ed9c9e24da1b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2cfbb2d26806acb38f93ce895bace4064311355c787c466059d697c41209d92f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T05:39:20Z",
    "title_canon_sha256": "50345caea557d9edcc86483cbf7797e07755b8bf420358a07b139454b546829b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14402",
    "kind": "arxiv",
    "version": 1
  }
}