The domination number of the k-token graph of the complete bipartite graph K_m,n

@misc{chinman2026domination,
  title = {{The domination number of the $k$-token graph of the complete bipartite graph $K_m,n$}},
  author = {Nathaniel Chinman and Antonio Cortijo and Beatrice Pedroni and Ian Seong and Lucy Stenger},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28936},
  eprint = {2610.28936},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28936},
}

TY  - UNPB
TI  - The domination number of the k-token graph of the complete bipartite graph K_m,n
AU  - Nathaniel Chinman
AU  - Antonio Cortijo
AU  - Beatrice Pedroni
AU  - Ian Seong
AU  - Lucy Stenger
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28936
UR  - https://arxiv.org/abs/2610.28936
AB  - 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≤ | X|. The k-token graph of G, denoted by F_k(G), is defined as follows. The vertex set 𝒳 consists of all k-subsets of X. Two vertices x,y∈ 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≥ 3.
ER  -