  The independence equivalence class of a graph $G$ is the set of graphs that
have the same independence polynomial as $G$. A graph whose independence
equivalence class contains only itself, up to isomorphism, is independence
unique. Beaton, Brown and Cameron (2019) showed that paths with an odd number
of vertices are independence unique and raised the problem of finding the
independence equivalence class of paths with an even number of vertices. The
problem is completely solved in this paper.
