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On the multiplicity of −1 as an eigenvalue of a tree with given number of pendant vertices
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-10-29 , DOI: 10.1080/03081087.2020.1838424 Xinlei Wang 1 , Dein Wong 1 , Liangli Wei 2 , Fenglei Tian 3
中文翻译:
作为具有给定数量下垂顶点的树的特征值的重数 -1
更新日期:2020-10-29
Linear and Multilinear Algebra ( IF 0.9 ) Pub Date : 2020-10-29 , DOI: 10.1080/03081087.2020.1838424 Xinlei Wang 1 , Dein Wong 1 , Liangli Wei 2 , Fenglei Tian 3
Affiliation
ABSTRACT
Let T be a tree with vertex set . The adjacency matrix of T is an matrix , where if is adjacent to and if otherwise. In this paper, we consider the multiplicity of as an eigenvalue of , which is written as . It is proved that among all trees T with pendant vertices, the maximum value of is p−1, and for a tree T with pendant vertices, if and only if with , or T is a tree in which for any pendant vertex v and any major vertex u of T, where a major vertex is a vertex of degree at least 3 and is the distance between v and u.
中文翻译:
作为具有给定数量下垂顶点的树的特征值的重数 -1
摘要
令T为一棵有顶点集的树. 邻接矩阵T是一个矩阵, 在哪里如果毗邻和否则。在本文中,我们考虑多重性作为特征值, 写成. 证明了在所有树T中悬垂顶点,最大值是p -1,并且对于具有垂饰顶点,当且仅当和, 或T是一棵树,其中对于T的任何下垂顶点v和任何主顶点u,其中主顶点是度数至少为 3 的顶点,并且是v和u之间的距离。