All eigenvalues of the blowup of a graph

Abstract

The $s$-blowup of a graph ($s\ge 2$) is the $2s$-uniform hypergraph obtained by replacing each vertex with a set of size $s$ and preserving the adjacency relation. In this paper, we define $2s$-weighted graphs and use them to give all eigenvalues of the $s$-blowup of a graph.