Signless Laplacian spectral radius of simplicial complexes without $r$-dimensional wheels
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908939741822976 |
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| author | Zhang, Huan-Zhi Fan, Yi-Zheng |
| author_facet | Zhang, Huan-Zhi Fan, Yi-Zheng |
| contents | An $r$-dimensional wheel is defined as the join of an $(r-2)$-simplex and a cycle. In this paper, we study the maximum signless Laplacian spectral radius of $n$-vertex $r$-dimensional pure simplicial complexes that contain no $r$-dimensional wheels. For sufficiently large $n$, we determine the extremal complexes that attain this maximum. Our result generalizes the corresponding extremal results of signless Laplacian on graphs and provides a spectral anlogue of a theorem of Sós, Erdős and Brown on the maximum number of facets of simplicial complexes in the case $r=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04536 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Signless Laplacian spectral radius of simplicial complexes without $r$-dimensional wheels Zhang, Huan-Zhi Fan, Yi-Zheng Combinatorics 05E45, 05C65, 05C35, 55U05 An $r$-dimensional wheel is defined as the join of an $(r-2)$-simplex and a cycle. In this paper, we study the maximum signless Laplacian spectral radius of $n$-vertex $r$-dimensional pure simplicial complexes that contain no $r$-dimensional wheels. For sufficiently large $n$, we determine the extremal complexes that attain this maximum. Our result generalizes the corresponding extremal results of signless Laplacian on graphs and provides a spectral anlogue of a theorem of Sós, Erdős and Brown on the maximum number of facets of simplicial complexes in the case $r=2$. |
| title | Signless Laplacian spectral radius of simplicial complexes without $r$-dimensional wheels |
| topic | Combinatorics 05E45, 05C65, 05C35, 55U05 |
| url | https://arxiv.org/abs/2604.04536 |