# Bound Graph Polysemy

### Abstract

*Bound polysemy * is the property of any pair $(G_1, G_2)$ of graphs on a shared vertex set $V$ for which there exists a partial order on $V$ such that any pair of vertices has an upper bound precisely when the pair is an edge in $G_1$ and a lower bound precisely when it is an edge in $G_2$. We examine several special cases and prove a characterization of the bound polysemic pairs that illuminates a connection with the squared graphs.