论文标题
合并的稳定指数和循环指数和均匀超图的笛卡尔产物
The stabilizing index and cyclic index of coalescence and Cartesian product of uniform hypergraphs
论文作者
论文摘要
令$ g $连接为统一的超图，让$ \ Mathcal {a}（g）$为$ g $的邻接张量。 $ g $的稳定指数是与光谱半径相关的$ \ MATHCAL {a}（g）$的特征向量的数量，而$ g $的循环指数是$ \ Mathcal {a}（g）$ lodulus等于频谱radius等于光谱的特征值的数量。令$ g_1 \ odot g_2 $和$ g_1 \ box g_2 $是连接的$ m $ suromriform hypergraphs $ g_1 $和$ g_2 $的合并和笛卡尔产品。在本文中，我们为$ g_1 \ odot g_2 $和$ g_1 \ box g_1 \ box g_2 $的稳定指数和周期性指数提供明确的公式。
Let $G$ be connected uniform hypergraph and let $\mathcal{A}(G)$ be the adjacency tensor of $G$. The stabilizing index of $G$ is the number of eigenvectors of $\mathcal{A}(G)$ associated with the spectral radius, and the cyclic index of $G$ is the number of eigenvalues of $\mathcal{A}(G)$ with modulus equal to the spectral radius. Let $G_1 \odot G_2$ and $G_1 \Box G_2$ 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 the stabilizing indices and cyclic indices of $G_1 \odot G_2$ and $G_1 \Box G_2$ in terms of those of $G_1$ and $G_2$ or the invariant divisors of their incidence matrices over $\mathbb{Z}_m$, respectively.
