The extremal spectral radii of -uniform supertrees
The extremal spectral radii of -uniform supertrees
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均匀超级树的极值谱半径
DOI：
10.1007/s10878-015-9896-4
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发表时间：
2016
影响因子：
1
通讯作者：
Qi Liqun
中科院分区：
文献类型：
--
作者：
Li Honghai;Shao Jia-Yu;Qi Liqun
本文研究了非一致超图的三种谱半径（邻接谱半径、无号Laplacian谱半径和关联谱半径）的极值问题。我们称连通的非循环一致超图为超树。本文介绍超图的“移动边”操作，以及这种操作的两种特殊情况：边释放操作和全嫁接操作。通过研究超图的这三种谱半径在这些操作下的扰动，证明了对于这三种谱半径，超图在顶点上的一致超树中唯一地达到最大谱半径.我们还确定了具有第二大谱半径的顶点上的唯一一致超树（对于这三种谱半径）。我们还证明了对于这三种谱半径，松弛路径唯一地达到顶点的所有次幂超树中的最小谱半径。给出了入射谱半径的一些界。讨论了入射谱半径与入射矩阵与其转置矩阵乘积的谱半径之间的关系。
In this paper, we study some extremal problems of three kinds of spectral radii of-uniform hypergraphs (the adjacency spectral radius, the signless Laplacian spectral radius and the incidence-spectral radius). We call a connected and acyclic-uniform hypergraph a supertree. We introduce the operation of “moving edges” for hypergraphs, together with the two special cases of this operation: the edge-releasing operation and the total grafting operation. By studying the perturbation of these kinds of spectral radii of hypergraphs under these operations, we prove that for all these three kinds of spectral radii, the hyperstarattains uniquely the maximum spectral radius among all-uniform supertrees onvertices. We also determine the unique-uniform supertree onvertices with the second largest spectral radius (for these three kinds of spectral radii). We also prove that for all these three kinds of spectral radii, the loose pathattains uniquely the minimum spectral radius among all-th power hypertrees ofvertices. Some bounds on the incidence-spectral radius are given. The relation between the incidence-spectral radius and the spectral radius of the matrix product of the incidence matrix and its transpose is discussed.