= Isoperimetric number of a graph
{title2=$i(G)=\min_{0<|A|\le|V(G)|/2}|\partial_eA|/|A|$}
= Isoperimetric number
{synonym}
For a finite <graph> with at least two <vertices>, the displayed minimum measures the fewest outgoing <edges> per vertex in a nonempty set occupying at most half the <graph>. It uses the <edge boundary>, rather than the <external vertex boundary>. For the <hypercube graph> $Q_n$, $n\ge1$, it equals one: edge-isoperimetry gives the lower bound and a coordinate half-cube attains it.
Back to article page
