{
  "abstract": "A set $S\\subseteq V(G)$ is a mutual-visibility set if every pair of vertices in $S$ is joined by a geodesic whose internal vertices do not belong to $S$. We define a reconfiguration graph whose vertices are the mutual-visibility sets of $G$. Two configurations are adjacent if one is obtained from the other by adding or removing one vertex or by sliding one token along an edge of $G$. The subgraphs induced by configurations of a fixed cardinality are called layers. The spanning subgraph formed by token-addition and token-removal edges is a daisy cube. We study the effects of token-sliding edges on distances and connectivity to this skeleton. For a connected host of order $n\\ge3$, the vertex connectivity of the reconfiguration graph lies between $3$ and $n$, and both bounds are attained. We determine several parameters of $\\mathcal{R}_{\\mathcal{M}}(K_n)$ and describe the behavior of the model for disconnected hosts and for isometric or convex subgraphs. We also give a component-based criterion for mobile mutual visibility. For complete bipartite graphs, we use a description of feasible configurations to determine connectivity and distance bounds for fixed-cardinality layers. For trees, we show that every component of a layer of cardinality at least three is isomorphic to a Cartesian product of subtrees, obtaining exact metric formulas and characterizing the connected layers. Finally, we prove that every layer of a cycle is connected.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24324",
  "author_total": 3,
  "authors": [
    {
      "name": "Julián A. Fresán-Figueroa"
    },
    {
      "name": "Ilán A. Goldfeder"
    },
    {
      "name": "Aldo Lozano-Piña"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3vdhwmcc5ngr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24324",
  "fulltext_url": null,
  "id": "b3vdhwmcc5ngr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24324",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7223057942",
  "pdf_url": "https://arxiv.org/pdf/2610.24324",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3vdhwmcc5ngr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24324",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24324"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Reconfiguration graphs of mutual-visibility sets",
  "title_text": "Reconfiguration graphs of mutual-visibility sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/b3vdhwmcc5ngr",
  "venue": "arXiv",
  "versions": []
}