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

TL;DR

This paper establishes an asymptotically tight upper bound for the domination number of the 2-token graph derived from path graphs, providing precise asymptotic behavior.

Contribution

It introduces the exact asymptotic upper bound for the domination number of the 2-token graph of path graphs, advancing understanding of token graph domination.

Findings

Domination number of 2-token path graphs is approximately n^2/10 plus lower order terms.

Provides an asymptotically tight upper bound for the domination number.

Enhances theoretical understanding of token graph domination properties.

Abstract

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 $\frac{n^2}{10}+\Theta(n)$.