In [1] Burger and Mynhardt introduced the idea of universal fixers. Let G = (V, E) be a graph with n vertices and G’ a copy of G. For a bijective function π: V(G) → V(G’), define the prism πG of G as follows: V(πG) = V(G) ∪ V(G’) and $E\left(\pi G\right)=E\left(G\right)\cup E\left(G^{\text{'}}\right)\cup M_{\pi }$, where $M_{\pi }=u\pi \left(u\right)\left|u\in V\right(G)$. Let γ(G) be the domination number of G. If γ(πG) = γ(G) for any bijective function π, then G is called a universal fixer. In [9] it is conjectured that the only universal fixers are the edgeless graphs K̅ₙ. In this work we generalize the concept of universal...