  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). In particular, we show that
the union of LPG and mLPG does not coincide with the whole class PCG, their
intersection is not empty, and that neither of the classes LPG and mLPG is
contained in the other. Finally, as the graphs we deal with belong to the more
general class of split matrogenic graphs, we focus on this class of graphs for
which we try to establish the membership to the PCG class.
