Edgeless graphs are the only universal fixers

Kirsti Wash

Given two disjoint copies of a graph $G$, denoted $G^1$ and $G^2$, and a permutation $\pi$ of $V(G)$, the graph $\pi G$ is constructed by joining $u\in V(G^1)$ to $\pi (u)\in V(G^2)$ for…