All graphs with at most seven vertices are Pairwise Compatibility Graphs

A graph G is called a pairwise compatibility graph (PCG) if there exists an edge-weighted tree T and two non-negative real numbers dmin and dmax such that each leaf lu of T corresponds to a vertex u∈V and there is an edge (u, v)∈E if and only if dmin ≤ dT,w (lu, lv) ≤ dmax, where dT,w (lu, lv) is the sum of the weights of the edges on the unique path from lu to lv in T. In this note, we show that ...