On the eigenvalues of trees
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 … Web6 de ago. de 2004 · Based on the above results, in this paper we give an upper bound for the largest eigenvalue of a tree T with n vertices, where T ≠ Sn, Gn(1), Gn(2), Gn(3), …
On the eigenvalues of trees
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Webeigenvalues of G, arranged in nondecreasing order, where n = V(G) . Since each row sum of L(G) is zero, μ1(G)=0. Recall that μn(G) ≤ n (see [1, 5]). Thus all Laplacian … Web1 de out. de 2024 · A Conjecture on Laplacian Eigenvalues of Trees. It is conjecture that for any tree T of order n ≥ 2, at least half of its Laplacian eigenvalues are less than \ …
Web1 de nov. de 2024 · If T is a tree of order n, where n = t k + 1, 2 ≤ k ≤ ⌊ n 2 ⌋, then λ k (T) ≤ t − 1, with equality if and only if T ∈ T (K 1, t − 1, k). In addition, there is a well-known fact … Web15 de dez. de 2015 · The purpose of the paper is to present quantitative estimates for the principal eigenvalue of discrete p-Laplacian on the set of rooted trees. Alternatively, it is studying the optimal constant of a class of weighted Hardy inequality. Three kinds of variational formulas in different formulation for the mixed principal eigenvalue of p …
Web204 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 … Web28 de set. de 2024 · Let G be a simple undirected graph. For real number α ∈ [0, 1], Nikiforov defined the A α -matrix of G as A α (G) = αD(G) + (1 − α)A(G), where A(G) and D(G) are the adjacency matrix and the degree diagonal matrix of G respectively. In this paper, we obtain a sharp upper bound on the largest eigenvalue ρ α (G) of A α (G) for α …
Web1 de ago. de 2008 · Let @l"1 (T) and @l"2 (T) be the largest and the second largest eigenvalues of a tree T, respectively. We obtain the following sharp lower bound for @l"1 (T): @l"1 (T)>=max {d"i+m"i-1}, where d"i is the degree of the vertex v"i and m"i is the average degree of the adjacent vertices of v"i. Equality holds if and only if T is a tree T …
WebSemantic Scholar extracted view of "On the Eigenvalues and Eigenvectors of a Class of Matrices" by S. Parter. Skip to search form Skip to main content ... mainly to R. C. Johnson and A. Leal Duarte on the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree. The techniques … Expand. 9. Highly Influenced. PDF. View 6 ... dave and bambi diamond editionWeb6 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…. … dave and bambi dave text to speechWeb23 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 unique tree which attains the maximal value of S ( T ) is determined.MSC:05C50. dave and bambi diamond wheelchairWebThe ε-eigenvalues of a graph Gare those of its eccentricity matrix ε(G). Wang et al [22] proposed the problem of determining the maximum ε-spectral radius of trees with given order. In this paper, we consider the above problem of n-vertex trees with given diameter. The maximum ε-spectral radius of n-vertex trees with fixed odd diameter is ... dave and bambi download gamebananaWebGiven a tree T , let q ( T ) be the minimum number of distinct eigenvalues in a symmetric matrix whose underlying graph is T . It is well known that q ( T ) ≥ d ( T )+1, where d ( T ) … black and brass coffee ownerWebMULTIPLICITIES 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. dave and bambi discord botWebThe Cayley tree has been widely used in solid state and statistical physics, as statistical mechanical models on it form a large class of exactly soluble models.[27,28]We find that the fidelity of the final state of the system and the target state in both the CTQW and the typical DTQW approach is less than unitary by analyzing the evolutionary process on the … black and brass coffee location