{
  "abstract": "This paper is about token graphs and domination number. Let $G=(X,E)$ denote an undirected graph that is connected, with no loops or multiple edges, vertex set $X$, and edge set $E$. Pick a positive integer $k\\leq \\vert X\\vert$. The $k$-token graph of $G$, denoted by $F_k(G)$, is defined as follows. The vertex set $\\mathcal{X}$ consists of all $k$-subsets of $X$. Two vertices $x,y\\in \\mathcal{X}$ are adjacent whenever the symmetric difference of $x$ and $y$ consists of two vertices that form an edge in $E$. In this paper, we compute the exact value for the domination number of $F_2(K_{m,n})$ where $K_{m,n}$ is the complete bipartite graph with parameters $m,n$. We present some bounds for the domination number of $F_k(K_{m,n})$ when $k\\geq 3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28936",
  "author_total": 5,
  "authors": [
    {
      "name": "Nathaniel Chinman"
    },
    {
      "name": "Antonio Cortijo"
    },
    {
      "name": "Beatrice Pedroni"
    },
    {
      "name": "Ian Seong"
    },
    {
      "name": "Lucy Stenger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cdh5y7p3bae2q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28936",
  "fulltext_url": null,
  "id": "cdh5y7p3bae2q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28936",
  "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": "W7223201905",
  "pdf_url": "https://arxiv.org/pdf/2610.28936",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cdh5y7p3bae2q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.28936",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28936"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The domination number of the $k$-token graph of the complete bipartite graph $K_{m,n}$",
  "title_text": "The domination number of the k-token graph of the complete bipartite graph K_m,n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/cdh5y7p3bae2q",
  "venue": "arXiv",
  "versions": []
}