Edge-isoperimetric inequalities for the symmetric product of graphs

Abstract

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arXiv commentThis paper has been withdrawn by the author. This paper has been merged into the article arXiv:1707.02446v4 (merged from arXiv:1612.08259 and arXiv:1707.02446v3)

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