On the two largest eigenvalues of trees
Weblength p – , q – , l – , respectively with common end vertices, where l ≥ q ≥ p ≥ and at most one of them is . Observe that any bicyclic graph G is obtained from a basic bicyclic graph ∞(p, q, l) or θ (p, q, l) by attaching trees to some of its vertices. For any bicyclic graph G, we call its basic bicyclic graph ∞(p, q, l) or θ (p, q, l) the kernel of G. WebWe give sharp lower bounds for the largest and the second largest distance eigenvalues of the k-th power of a connected graph, determine all trees and unicyclic graphs for which the second largest distance eigenvalues of the squares are less than 5 - 3 ...
On the two largest eigenvalues of trees
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Web23 de jun. de 2014 · For S ( T ) , the sum of the two largest Laplacian eigenvalues of a tree T, an upper bound is obtained. Moreover, among all trees with n ≥ 4 vertices, the … Web25 de jun. de 2024 · Every tree that is not a path has a vertex of degree at least three where at least two pendant paths are attached. Every tree can be transformed into a path by a sequence of π-transformations. In [ 5 ], Braga, Rodrigues and Trevisan show the interesting effect of π -transformations on the distribution of Laplacian eigenvalues.
Web12 de jan. de 2015 · The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, M 1 , was understood fully (froma combinatorial perspective) by C.R. Johnson, A. Leal-Duarte (Linear Algebra and Multilinear Algebra 46 (1999) 139-144). Among the possible multiplicity lists for the eigenvalues of Hermitian matrices whose graph is a tree, we … Webequal to 1 for each row and each column. The ε-eigenvalues of a graph Gare those of its eccentricity matrix ε(G). Wang et al [22] proposed the problem of determining the …
Web1 de mar. de 1973 · PDF On Mar 1, 1973, L. Lovász and others published On the Eigenvalue of Trees Find, read and cite all the research you need on ResearchGate WebIn [2], Hagos showed that a graphG has exactly two main eigenvalues if and only if G is 2-walk linear. Moreover, if G is a 2-walk(a,b)-linear connected graph, then the two main eigenvaluesλ1,λ2 of G are λ1,2 = a± √ a2+4b 2,i.e., one has λ1 +λ2 = a,λ1λ2 =−b.Hence, in order to find all graphs with exactly two main eigenvalues, it is ...
Web6 de ago. de 2004 · On the largest eigenvalues of trees. ☆. 1. Introduction. In this article, we consider only connected finite simple graphs, in particular, trees. Let G be a graph …
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. iphone pro max 12 price south africaWeb2 de jul. de 2016 · On the Two Largest Eigenvalues of Trees M. Hofmeister Siemens AG Corporate Research & Development D-81 730 Munich, Germany Submitted by Richard A. Brddi ABSTRACT Very little is known about upper bounds for the largest eigenvalues of a tree that depend only on the vertex number. Starting from a classical upper bound for the … orange county nc swcdWebW. Lin and X. Guo/On the largest eigenvalues of trees with perfect matchings 1061 We will use α0,α2 0,α ∗ 0,α1,β,γtransformations and e.g.t to compare the largest eigenvalues of two trees in T2m. Note that if a tree T has a perfect match-ing, then T has a unique perfect matching. Denote the unique perfect match-ing of T by M(T). orange county nc shiipWebScribd is the world's largest social reading and publishing site. 5. FLOOR PLACEMENTS. Uploaded by ... the minimum Steiner tree is between one and two times the half-perimeter measure [ Hanan, 1966]. ... the x - and y -coordinates are given by the eigenvectors corresponding to the two smallest, nonzero, eigenvalues. orange county nc tax officeWeb204 Y. Hou, J. Li / Linear Algebra and its Applications 342 (2002) 203–217 graph-theoretic properties of G and its eigenvalues. Up to now, the eigenvalues of a tree T with a perfect matching have been studied by several authors (see [2,7,8]). However, when a tree has no perfect matching but has an m-matching M, namely, M consists of m mutually … orange county nc tax gisWebFor , the sum of the two largest Laplacian eigenvalues of a tree T, an upper bound is obtained. Moreover, among all trees with iphone pro max 13 1tb priceWeb21 de jun. de 2024 · Graph_2nd_Largest_Eigenvalue, etc., up to Graph_5th_Largest_Eigenvalue), and the spectral gap (the difference between the moduli of the two largest eigenvalues) of the adjacency matrix (Graph_Spectral_Gap). For brevity of notation, we refer with “eigenvalue of a graph” to the eigenvalue of its adjacency matrix. orange county nc tax