Pairwise compatibility graph

A graph $G$ is a Pairwise Compatibility Graph (PCG) if there exists a tree $T$ and two non-negative real numbers $d_{min}<d_{max}$ such that each node $u'$ of $G$ has a one-to-one mapping with a leaf $u$ of $T$ such that two nodes $u'$ and $v'$ are adjacent in $G$ if and only if the distance between $u$ and $v$ are in the interval $[d_{min},d_{max}]$.

The subclasses of PCG include graphs of at most seven vertices, cycles, forests, complete graphs, interval graphs, etc. The computational complexity of recognizing a graph as PCG is still unknown.