{
  "abstract": "We study graphs whose powers are well-covered, with an emphasis on Cartesian products and Cayley graphs. We first establish necessary conditions and sufficient criteria for Cartesian products, provide examples showing that a factor need not be well-covered and that two noncomplete factors can have the well-covered powers property, and classify several structured product families. In particular, we construct graphs satisfying the well-covered powers property for arbitrarily large diameters. We then show that the Cartesian square of a connected abelian Cayley graph is well-covered exactly when the graph is complete. We classify the well-covered-power graphs among connected circulant graphs of degree at most four. For Cartesian products of any number of complete graphs, we also prove that the recursive alphabet-size inequalities in the final conjecture are sufficient for all powers to be well-covered, prove partial converses for arbitrarily many factors, and give explicit obstructions for every binary prefix followed by one complete factor.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03956",
  "author_total": 3,
  "authors": [
    {
      "name": "Haobo Ma"
    },
    {
      "name": "Thanh Vu"
    },
    {
      "name": "Wenlin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ekb731s4d9c97.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03956",
  "fulltext_url": null,
  "id": "ekb731s4d9c97",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03956",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03956",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ekb731s4d9c97.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03956",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03956"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Well-Covered Powers: Cartesian Products and Cayley Graphs",
  "title_text": "Well-Covered Powers: Cartesian Products and Cayley Graphs",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/ekb731s4d9c97",
  "venue": "arXiv",
  "versions": []
}