Author

E. Troncoso

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Preprint Oct 2026

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

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...

E. Troncoso, I. Caldera, L. M. Rivera · 0 citations

Preprint Oct 2026

The domination number of the $2$-token graph of path graphs

We prove that the domination number of the $2$-token graph of the path $P_n$ is $\gamma(F_2(P_n))=d(n)$ for every $n\ge 13$, where $d(n)=\frac1{10}(n^2+5n+c)$ and $c$ is an explicit constant that depends on $n \bmod 5$. This settles a conjecture by Lea\~nos and the authors, who previously proved the upper bound. The lo...

E. Troncoso, L. M. Rivera · 0 citations