{
  "annotation_id": "384d4809-c3af-44a9-973e-313d615f85d8",
  "date_created": "2026-03-02T18:02:17.286000Z",
  "date_modified": "2026-03-02T18:02:17.286000Z",
  "file_hash": "772398bdaf9af7c20d67160f8eb135bd87980d4b15ae6d20cf7eda1e33950e5d",
  "private": false,
  "record": {
    "abstract": "We use the line digraph construction to associate an orthogonal matrix with\neach graph. From this orthogonal matrix, we derive two further matrices. The\nspectrum of each of these three matrices is considered as a graph invariant.\nFor the first two cases, we compute the spectrum explicitly and show that it is\ndetermined by the spectrum of the adjacency matrix of the original graph. We\nthen show by computation that the isomorphism classes of many known families of\nstrongly regular graphs (up to 64 vertices) are characterized by the spectrum\nof this matrix. We conjecture that this is always the case for strongly regular\ngraphs and we show that the conjecture is not valid for general graphs. We\nverify that the smallest regular graphs which are not distinguished with our\nmethod are on 14 vertices.",
    "arxiv_id": "quant-ph/0505026",
    "authors": [
      "David Emms",
      "Edwin R. Hancock",
      "Simone Severini",
      "Richard C. Wilson"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "The Electronic Journal of Combinatorics 13 (2006), #R34",
    "title": "A matrix representation of graphs and its spectrum as a graph invariant",
    "url": "https://arxiv.org/abs/quant-ph/0505026"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b9ec3a5c-db65-4f81-a3d9-8d7c6286bece",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}