All Graphs with at Most Seven Vertices are Pairwise Compatibility Graphs
نویسندگان
چکیده
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 all the graphs with at most seven vertices are PCGs. In particular all these graphs except for the wheel on 7 vertices W7 are PCGs of a particular structure of a tree: a centipede.
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عنوان ژورنال:
- Comput. J.
دوره 56 شماره
صفحات -
تاریخ انتشار 2013