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A graph $G$ is called a pairwise compatibility graph (PCG) if there exists anedge-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 $d_{min} \leq d_{T,w} (l_u,l_v) \leq d_{max}$ where $d_{T,w} (l_u, l_v)$ is the sum of the weights of theedges on the unique path from $l_u$ to $l_v$ in $T$.  In this note, we show that all the graphs with at most seven vertices arePCGs. In particular all these graphs except for the wheel on 7 vertices $W_7$are PCGs of a particular structure of a tree: a centipede.

All graphs with at most seven vertices are Pairwise Compatibility Graphs