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About: Pairwise compatibility graph     Goto   Sponge   NotDistinct   Permalink

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In graph theory, a graph is a pairwise compatibility graph (PCG) if there exists a tree and two non-negative real numbers such that each node of has a one-to-one mapping with a leaf node of such that two nodes and are adjacent in if and only if the distance between and are in the interval . The subclasses of PCG include graphs of at most seven vertices, cycles, forests, complete graphs, interval graphs and ladder graphs. However, there is a graph with eight vertices that is known not to be a PCG.