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arXiv · 2610.11265

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

Emmanuel Acosta Troncoso·Luis Manuel Rivera
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Abstract

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 $n\ge 13$, 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 Leaños and the authors, who previously proved the upper bound. The lower bound is computer-assisted and follows the method used by Gonçalves, Pinlou, Rao and Thomassé for grid graphs.

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Emmanuel Acosta Troncoso, Luis Manuel Rivera. 2026-10-08. The domination number of the $2$-token graph of path graphs. https://arxiv.org/abs/2610.11265

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