E. Troncoso

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math.CO2026

Token graphs of stars

Emmanuel Acosta Troncoso, César Hernández-Cruz, Ana Trujillo-Negrete

The $k$ -token graph $F_{k} (G)$ of a graph $G$ has as vertices the $k$ -subsets of $V (G)$ , two of them being adjacent when their symmetric difference is an edge of $G$ . Let $S_{n}$ be th…

math.CO2026

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

E. Acosta Troncoso, I. Caldera Caldera, L. M. Rivera

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 th…

math.CO2026

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

Emmanuel Acosta Troncoso, Luis Manuel Rivera

We prove that the domination number of the $2$ -token graph of the path $P_{n}$ is $γ (F_{2} (P_{n})) = d (n)$ for every $n \geq 13$ , where $d (n) = \frac{1}{10} (n^{2} + 5 n + c)$ and $c$ is an explicit con…

math.CO2026

An asymptotically tight upper bound for the domination number of the $2$ -token graph of path graphs

E. Acosta Troncoso, J. Leaños, L. M. Rivera

In this note, we show that the domination number of the $2$ -token graph of the path graph of order $n \geq 2$ is equal to $\frac{n ^{2}}{10} + Θ (n)$ .

Token graphs of stars

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

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

An asymptotically tight upper bound for the domination number of the 2-token graph of path graphs

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

An asymptotically tight upper bound for the domination number of the $2$ -token graph of path graphs