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PreprintCC BY 4.0arXiv

Spectral moments and characteristic polynomials of vertex expansion hypergraphs of graphs

  • Ge Lin
  • Changjiang Bu
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Abstract

The s-vertex expansion hypergraph G[s] is the 2s-uniform hypergraph obtained by replacing each vertex of a graph G with s new vertices. A closed walk in G is called an s-multiple closed walk if the number of times it arrives at each vertex of G is divisible by s. In this paper, we obtain an expression for the spectral moments of G[s] in terms of s-multiple closed walks in G. Using these spectral moments, we give the characteristic polynomial of G[s].

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Cite

BibTeXRIS
BibTeX
@misc{lin2026spectral,
  title = {{Spectral moments and characteristic polynomials of vertex expansion hypergraphs of graphs}},
  author = {Ge Lin and Changjiang Bu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05897},
  eprint = {2609.05897},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05897},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Spectral moments and characteristic polynomials of vertex expansion hypergraphs of graphs
AU  - Ge Lin
AU  - Changjiang Bu
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.05897
UR  - https://arxiv.org/abs/2609.05897
AB  - The s-vertex expansion hypergraph G^[s] is the 2s-uniform hypergraph obtained by replacing each vertex of a graph G with s new vertices. A closed walk in G is called an s-multiple closed walk if the number of times it arrives at each vertex of G is divisible by s. In this paper, we obtain an expression for the spectral moments of G^[s] in terms of s-multiple closed walks in G. Using these spectral moments, we give the characteristic polynomial of G^[s].
ER  -