| 摘要: |
| 本文研究固定顶点数与直径的~$k$-一致单圈超图的谱极值刻画问题。利用超图谱特征方程、移边变换与单圈超图结构分类方法，分析超图在直径约束下的谱半径变化规律。完整刻画了~$n$~个顶点、直径为~$d$~的~$k$-一致单圈超图中谱半径达到最大值的唯一极图结构。将~Liu~ 等人关于普通单圈图的谱极值经典结论推广至~$k$-一致单圈超图。 |
| 关键词: 单圈一致超图 超图张量谱 谱半径 直径 |
| DOI： |
| 分类号:O157.5 |
| 基金项目:国家自然科学基金项目(12161073) |
|
| Spectral extremal characterization of unicyclic uniform hypergraphs with fixed diameter |
|
niu qiannan
|
| Abstract: |
| This paper investigates the extremal characterization of spectral radii of $k$-uniform unicyclic hypergraphs with fixed vertex number and diameter. Using spectral characteristic equations of hypergraphs, edge shifting operations and structural classification of unicyclic hypergraphs, we analyze how the spectral radius varies under diameter constraints. We fully characterize the unique extremal structure attaining the maximum spectral radius among all such hypergraphs. We extend the classical spectral extremal results on unicyclic graphs established by Liu et al. to $k$-uniform unicyclic hypergraphs. |
| Key words: Unicyclic uniform hypergraphs Tensor spectra of hypergraphs Spectral radius Diameter |
