A graph $G$ is called a pairwise compatibility graph (PCG) if there exists an
edge weighted tree $T$ and two non-negative real numbers $d_{min}$ and
$d_{max}$ such that each leaf $l_u$ of $T$ corresponds to a vertex $u \in V$
and there is an edge $(u,v) \in E$ if and only if $d_{min} \leq d_T (l_u, l_v)
\leq d_{max}$ where $d_T (l_u, l_v)$ is the sum of the weights of the edges on
the unique path from $l_u$ to $l_v$ in $T$. In this paper we analyze the class
of PCG in relation with two particular subclasses resulting from the the cases
where $\dmin=0$ (LPG) and $\dmax=+\infty$ (mLPG).