Pith Number

pith:57ZTWLYX

pith:2026:57ZTWLYXUS3SGA7P7S2FOYPCGF

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On the Eccentricity Laplacian and Eccentricity Signless Laplacian Matrices of a Graph

Anubha Jindal, Keshav Saini, K. Palpandi

The eccentricity Laplacian and signless Laplacian matrices share the same spectrum as the eccentricity matrix for multiple graph classes and characterize E-bipartite graphs via spectral symmetry.

arxiv:2605.14508 v1 · 2026-05-14 · math.CO

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\pithnumber{57ZTWLYXUS3SGA7P7S2FOYPCGF}

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

We establish the equivalence among the eccentricity Laplacian, eccentricity signless Laplacian, and eccentricity spectrum for different classes of graphs. We provide spectral characterization of E-bipartite graphs by the symmetry of E-spectrum and the similarity of these Laplacian matrices.

C2weakest assumption

All graphs under consideration are connected, so that every pair of vertices has a finite eccentricity and the eccentricity matrix is well-defined with no infinite entries.

C3one line summary

Introduces eccentricity Laplacian and signless Laplacian matrices, establishes their spectral equivalences for graph classes, and characterizes E-bipartite graphs via spectrum symmetry and matrix similarity.

References

20 extracted · 20 resolved · 0 Pith anchors

[1] Aouchiche, M., & Hansen, P. (2013). Two Laplacians for the distance matrix of a graph.Linear Algebra and its Applications, 439(1), 21-33. https://doi.org/10.1016/j.laa.2013.02.030 2013 · doi:10.1016/j.laa.2013.02.030

[2] Some properties of the distance Laplacian eigen- values of a graph.Czech Math J64, 751-761 2014 · doi:10.1007/s10587-014-

[3] L-structured quaternion matrices and quaternion linear matrix equations 2016 · doi:10.1080/03081087.2015.1073215

[4] Aouchiche, M., & Hansen, P. (2017). Distance Laplacian Eigenval- ues and Chromatic Number in Graphs.Filomat, 31(9), 2545-2555. http://www.jstor.org/stable/26194990 2017

[5] Nath, M., & Paul, S. (2014). On the distance Laplacian spectra of graphs.Linear Algebra and its Applications, 460, 97-110. https://doi.org/10.1016/j.laa.2014.07.025 2014 · doi:10.1016/j.laa.2014.07.025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:06.226741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eff33b2f17a4b72303effcb45761e23140a9e5758d98f26685b3ccd2f9833dbf

Aliases

arxiv: 2605.14508 · arxiv_version: 2605.14508v1 · doi: 10.48550/arxiv.2605.14508 · pith_short_12: 57ZTWLYXUS3S · pith_short_16: 57ZTWLYXUS3SGA7P · pith_short_8: 57ZTWLYX

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/57ZTWLYXUS3SGA7P7S2FOYPCGF \
  | 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: eff33b2f17a4b72303effcb45761e23140a9e5758d98f26685b3ccd2f9833dbf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "014dc88356c561c02a3f2ff631780aa27c4dbb2b43644611e27d2c2a09b98aab",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T07:52:31Z",
    "title_canon_sha256": "f95b44bb8e90144db6f7f4fdd03c5b690a328c09399681d2ac1ab4e339820154"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14508",
    "kind": "arxiv",
    "version": 1
  }
}