论文标题
构建具有相同光谱半径和匹配能量的$ R $均匀超级树
Constructing the $r$-uniform supertrees with the same spectral radius and matching energyv
论文作者
论文摘要
$ r $均匀的超级树是一个连接和无环的超图，每个边缘都有$ r $ pertices，其中$ r \ geq 3 $。我们提出了与$ r $均匀的超图相匹配的概念，该概念定义为其匹配多项式的所有特征值的绝对值之和。借助$ R $均匀超级树的匹配多项式，构建了三对具有相同光谱半径和相同匹配能量的$ R $均匀的超级树，并且具有相同的光谱半径和相同的匹配能量的两个无限的匹配能量，并且具有相同的频谱半径。关于与它们的邻接矩阵有关的图形的一些已知结果可以自然地从我们的新结果中推导。
An $r$-uniform supertree is a connected and acyclic hypergraph of which each edge has $r$ vertices, where $r\geq 3$. We propose the concept of matching energy for an $r$-uniform hypergraph, which is defined as the sum of the absolute value of all the eigenvalues of its matching polynomial. With the aid of the matching polynomial of an $r$-uniform supertree, three pairs of $r$-uniform supertrees with the same spectral radius and the same matching energy are constructed, and two infinite families of $r$-uniform supertrees with the same spectral radius and the same matching energy are characterized. Some known results about the graphs with the same spectra regarding to their adjacency matrices can be naturally deduced from our new results.
