WebEIGENVALUES OF TREES 45 Many of the trees which appear in the following will obtain an s-claw for a positive integer s, that is, a vertex x adjacent to s vertices of degree 1. This will be drawn as 2. THE LARGEST EIGENVALUE OF A TREE As mentioned in the introduction, h, < &T for any tree T with n vertices. WebMULTIPLICITIES OF EIGENVALUES OF A TREE 3 A tree is a connect graph without cycles and a forest is a graph in each component is a tree. In this paper we consider finite graphs possibly with loops (i.e., (i,i) may be an edge). If to each edge (i,j) is assigned a complex number, we have a weighted graph. We shall focus our attention on trees.
On the multiplicities of eigenvalues of a Hermitian matrix whose …
Web1 de fev. de 2010 · Bounds on the k th eigenvalues of trees and forests. Linear Algebra Appl., 149 (1991), pp. 19-34. Article. Download PDF View Record in Scopus Google Scholar. J.M. Guo, S.W. Tan. A relation between the matching number and Laplacian spectrum. Linear Algebra Appl., 325 (2001), pp. 71-74. Web1 de jun. de 2004 · In [6], Guo and Tan have shown that 2 is a Laplacian eigenvalue of any tree with perfect matchings. For trees without perfect matchings, we study whether 2 is one of its Laplacian eigenvalues. If the matching number is 1 or 2, the answer is negative; otherwise, there exists a tree with that matching number which has (has not) the … read this your gay
On the number of Laplacian eigenvalues of trees smaller than two
Web6 de nov. de 2013 · On the distribution of Laplacian eigenvalues of a graph. J. Guo, Xiao Hong Wu, Jiong-Ming Zhang, Kun-Fu Fang. Mathematics. 2011. This paper presents some bounds on the number of Laplacian eigenvalues contained in various subintervals of [0, n] by using the matching number and edge covering number for G, and asserts that for a…. … Web15 de fev. de 2002 · Very little is known about upper bound for the largest eigenvalue of a tree with a given size of matching. In this paper, we find some upper bounds for the … Webis real symmetric its eigenvalues are real. A graph G is called integral if all its eigenvalues are integers. In this paper, a graph is always a tree, i.e., a connected, acyclic graph. It is well-known that if λis an eigenvalue of a tree T, then −λis also an eigenvalue ([2], Lemma 1). Eigenvalues of trees have been studied in [8–12]. how to store celery sticks