{
  "abstract": "For a graph $G$, the $2$-token graph $F_2(G)$ has as vertices all $2$-subsets of $V(G)$, with two such subsets adjacent whenever their symmetric difference is an edge of $G$. In this paper, we determine the domination number of the $2$-token graph of the complete bipartite graph $K_{m,n}$, for all integers $2\\le m\\le n$. We show that it equals $\\lceil m/2\\rceil+n-1$, except when $m=3$, or when $m\\ge5$ is odd and $n=m+1$; in these two exceptional situations it is one less. Our arguments rely on an explicit characterization of the dominating sets of the $2$-token graph of $K_{m,n}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31557",
  "author_total": 3,
  "authors": [
    {
      "name": "E. Acosta Troncoso"
    },
    {
      "name": "I. Caldera Caldera"
    },
    {
      "name": "L. M. Rivera"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8t3j5kgvs0qsn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31557",
  "fulltext_url": null,
  "id": "8t3j5kgvs0qsn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31557",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7223412677",
  "pdf_url": "https://arxiv.org/pdf/2610.31557",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8t3j5kgvs0qsn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31557",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31557"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The domination number of the 2-token graph of the complete bipartite graph",
  "title_text": "The domination number of the 2-token graph of the complete bipartite graph",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/8t3j5kgvs0qsn",
  "venue": "arXiv",
  "versions": []
}