Edge isoperimetric inequalities for the symmetric product of graphs
The $k$ th symmetric product of a graph $G$ with vertex set $V$ with edge set $E$ is a graph with vertices as $k$ sets of $V$ where two $k$ sets are connected by an edge if and only if their symmetric difference is an edge in $E$ Using the isoperimetric properties of the vertex induced subgraphs of $G$ and Sobolev inequalities on graphs, we obtain various edge isoperimetric inequalities pertaining to the symmetric product of certain families of finite and infinite graphs.
ArXiv