  A graph $G=(V,E)$ is a pairwise compatibility graph (PCG) if there exists an
edge-weighted tree $T$ and two non-negative real numbers $d_{min}$ and
$d_{max}$, $d_{min} \leq d_{max}$, such that each node $u \in V$ is uniquely
associated to a leaf of $T$ and there is an edge $(u,v) \in E$ if and only if
$d_{min} \leq d_{T} (u, v) \leq d_{max}$, where $d_{T} (u, v)$ is the sum of
the weights of the edges on the unique path $P_{T}(u,v)$ from $u$ to $v$ in
$T$. Understanding which graph classes lie inside and which ones outside the
PCG class is an important issue. In this paper we propose a new proof technique
that allows us to show that some interesting classes of graphs have empty
intersection with PCG. As an example, we use this technique to show that wheels
and graphs obtained as strong product between a cycle and $P_2$ are not PCGs.
