论文标题
带有切割顶点的均匀超图的痕迹和埃斯特拉达指数
The trace and Estrada index of uniform hypergraphs with cut vertices
论文作者
论文摘要
令$ \ mathcal {h} $为$ m $均匀的超图，然后让$ \ Mathcal {a}（\ Mathcal {h}）$为$ \ Mathcal {h} $的邻接张量，可以将其视为同质性的多种元素系统的系统。 Morozov和Shakirov将线性系统的痕迹概括为非线性均匀的多项式系统，并获得了多维结果剂的明确公式。 Sun，Zhou和Bu引入了均匀的超图的埃斯特拉达指数，该指数与其邻接张量的痕迹密切相关。在本文中，我们给出$ \ Mathcal {a}（\ Mathcal {h}）$的痕迹时的公式，当$ \ Mathcal {h} $包含剪切的顶点，并在$ \ MATHCAL {H} $时在本地变化下遇到$ \ Mathcal {H}时在痕迹上获得结果。我们证明，在所有边缘数量固定数量的高速公司中，超速path是具有最小estrada索引的唯一一个，而Hyperstar是具有最大estrada索引的唯一一个。
Let $\mathcal{H}$ be an $m$-uniform hypergraph, and let $\mathcal{A}(\mathcal{H})$ be the adjacency tensor of $\mathcal{H}$ which can be viewed as a system of homogeneous polynomials of degree $m-1$. Morozov and Shakirov generalized the traces of linear systems to nonlinear homogeneous polynomial systems and obtained explicit formulas for multidimensional resultants. Sun, Zhou and Bu introduced the Estrada index of uniform hypergraphs which is closely related to the traces of their adjacency tensors. In this paper we give formulas for the traces of $\mathcal{A}(\mathcal{H})$ when $\mathcal{H}$ contains cut vertices, and obtain results on the traces and Estrada index when $\mathcal{H}$ is perturbed under local changes. We prove that among all hypertrees with fixed number of edges, the hyperpath is the unique one with minimum Estrada index and the hyperstar is the unique one with maximum Estrada index.
