منابع مشابه
Some Spectral Properties of Starlike Trees
A b s t r a c t. A tree is said to be starlike if exactly one of its vertices has degree greater than two. We show that almost all starlike trees are hyperbolic, and determine all exceptions. If k is the maximal vertex degree of a starlike tree and λ 1 is its largest eigenvalue, then √ k ≤ λ 1 < k/ √ k − 1. A new way to characterize integral starlike trees is put forward.
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The reverse Wiener index of a connected graph G is defined as Λ(G) = 1 2 n(n− 1)d−W (G), where n is the number of vertices, d is the diameter, and W (G) is the Wiener index (the sum of distances between all unordered pairs of vertices) of G. We determine the n-vertex non-starlike trees with the first four largest reverse Wiener indices for n > 8, and the nvertex non-starlike non-caterpillar tre...
متن کاملThe Dirichlet spectral radius of trees
In this paper, the trees with the largest Dirichlet spectral radius among all trees with a given degree sequence are characterized. Moreover, the extremal graphs having the largest Dirichlet spectral radius are obtained in the set of all trees of order n with a given number of pendant vertices.
متن کاملLexicographical ordering by spectral moments of trees with a given bipartition
Lexicographic ordering by spectral moments ($S$-order) among all trees is discussed in this paper. For two given positive integers $p$ and $q$ with $pleqslant q$, we denote $mathscr{T}_n^{p, q}={T: T$ is a tree of order $n$ with a $(p, q)$-bipartition}. Furthermore, the last four trees, in the $S$-order, among $mathscr{T}_n^{p, q},(4leqslant pleqslant q)$ are characterized.
متن کاملThe integral trees with spectral radius 3
There are 11 integral trees with largest eigenvalue 3.
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ژورنال
عنوان ژورنال: Linear and Multilinear Algebra
سال: 2018
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081087.2018.1524435