Spectral radius of $2$-dimensional simplicial complexes with given Betti number

Chuan-Ming She; Yi-Zheng Fan; Yi-Min Song

Spectral radius of $2$-dimensional simplicial complexes with given Betti number

Combinatorics 2026-01-14 v1

Authors: Chuan-Ming She , Yi-Zheng Fan , Yi-Min Song

Abstract

In this paper we establish an asymptotic formula for the signless Laplacian spectral radius of a $2$ -dimensional simplicial complex with given $2$ -th Betti number. Furthermore, we characterize the $2$ -dimensional simplicial complex that achieves the maximum signless Laplacian spectral radius among all-dimensional simplicial complex with the $2$ -th Betti number equal to $1$ or $2$ .

Keywords

spectral radius simplicial complex betti number signless laplacian asymptotic formula extremal problem

Cite

@article{arxiv.2601.08171,
  title  = {Spectral radius of $2$-dimensional simplicial complexes with given Betti number},
  author = {Chuan-Ming She and Yi-Zheng Fan and Yi-Min Song},
  journal= {arXiv preprint arXiv:2601.08171},
  year   = {2026}
}

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