All eigenvalues of the blowup of a graph

Ge Lin; Changjiang Bu

All eigenvalues of the blowup of a graph

Combinatorics 2026-02-16 v1

Authors: Ge Lin , Changjiang Bu

Abstract

The $s$ -blowup of a graph ( $s\geq2$ ) 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.

Keywords

graph blowup eigenvalues weighted graphs hypergraph spectral graph theory

Cite

@article{arxiv.2602.12654,
  title  = {All eigenvalues of the blowup of a graph},
  author = {Ge Lin and Changjiang Bu},
  journal= {arXiv preprint arXiv:2602.12654},
  year   = {2026}
}

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