= Plünnecke graph
{c}
A finite directed graph with layers $V_0,\ldots,V_n$ and edges only to the next layer is a Plünnecke graph when every edge $u\to v$ permits both commutation matchings. The successors of $v$ inject into the successors of $u$ through edges to the original successors; the predecessors of $u$ inject into those of $v$ through edges from the original predecessors. These conditions formalize interchanging adjacent summands in an additive graph. They persist on channels consisting of paths between prescribed endpoint sets.
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