The domination number of the 2-token graph of the complete bipartite graph

@misc{troncoso2026domination,
  title = {{The domination number of the 2-token graph of the complete bipartite graph}},
  author = {E. Acosta Troncoso and I. Caldera Caldera and L. M. Rivera},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31557},
  eprint = {2610.31557},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31557},
}

TY  - UNPB
TI  - The domination number of the 2-token graph of the complete bipartite graph
AU  - E. Acosta Troncoso
AU  - I. Caldera Caldera
AU  - L. M. Rivera
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31557
UR  - https://arxiv.org/abs/2610.31557
AB  - 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≤ m≤ n. We show that it equals ⌈ m/2⌉+n−1, except when m=3, or when m≥5 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.
ER  -