Let G be connected uniform hypergraph and let $\mathcal{A}(G)$ be the adjacency tensor of G. The stabilizing index of G is exactly the number of eigenvectors of $\mathcal{A}(G)$ associated with the spectral radius, and the cyclic index of G is exactly the number of eigenvalues of $\mathcal{A}(G)$ with modulus equal to the spectral radius. Let $G_1\odot G_2$ and $G_1\square G_2$ be the coalescence and Cartesian product of connected m-uniform hypergraphs $G_1$ and $G_2$ respectively. In this paper, we give explicit formulas for the stabilizing indices and cyclic indices of $G_1\odot G_2$ and $G_1\square G_2$ in terms of those of $G_1$ and $G_2$ or the invariant divisors of their incidence matrices over ${\mathbb{Z}}_m$, respectively.

中文翻译：

---

均匀超图的聚结和笛卡尔积的稳定指数和循环指数

令G连接均匀超图并令$\mathcal{一种}(G)$是G的邻接张量。G的稳定指数正好是$\mathcal{一种}(G)$与谱半径相关联，而G的循环索引正是$\mathcal{一种}(G)$模数等于谱半径。让$G_1\odot G_2$ 和 $G_1\square G_2$是连接的m -均匀超图的合并和笛卡尔积$G_1$ 和 $G_2$分别。在本文中，我们给出了稳定指数和循环指数的明确公式$G_1\odot G_2$ 和 $G_1\square G_2$ 就那些 $G_1$ 和 $G_2$ 或者它们的关联矩阵的不变因数 ${\mathbb{Z}}_{米}$， 分别。