On the eigenvalues of trees
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 unique tree which attains the maximal value of S ( T ) is determined.MSC:05C50. 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].
On the eigenvalues of trees
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WebThe 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 ... WebIt is shown that the generalized tree shift increases the largest eigenvalue of the adjacency matrix and Laplacian matrix, decreases the coefficients of the …
Webtree algorithm for obtaining a diagonal matrix congruent to A+xIn, x ∈ R, and explain its use in finding eigenvalues of trees. The Laplacian matrix and the algorithm’s Laplacian analog are given in Section 4, along with some classic theorems involving Laplacian eigenvalues. Finally, in Section 5 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 …
Web† It has 2000 spanning trees, the most of any 3-regular graph on 10 vertices. To compute the eigenvalues of the Petersen graph, we use the fact that it is strongly regular . This means that not only does each vertex have the same degree (3), but each pair of vertices 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 2010 · Let T be a tree with 1 as an eigenvalue of multiplicity k. If T /= K 2 or Y 6 then T has k + 1 pendant edges that form an induced matching. Proof. Suppose that T is …
WebThus all its eigenvalues are real. The positive inertia index (resp. the negative inertia index) of a mixed graph Ge, denoted by p+(Ge)(resp. n−(Ge)), is defined to be the number of positive eigenvalues (resp. negative eigenvalues) of H(Ge). The rank of a mixed graph Ge, denoted by r(Ge), is exactly the sum of p+(Ge)and n−(Ge). The hyper-v share folder with guestWebSemantic 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 ... hyper-v snapshot locationWeb1 de jan. de 2024 · For some given number c < − 2 2, which trees with least eccentricity eigenvalues are in [c, − 2 2)? In this paper, we characterize the extremal trees having … hyper-v state is yet to be initializedWeb15 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 … hyper-v sound deviceWebKeywords Eigenvalues · Graph · Tree · Symmetric matrices · Vertex degrees Mathematics Subject Classification (2000) 15A18 · 15A57 · 05C50 · 05C05 · 05C12 1 Introduction In recent years, the interest of study on the multiplicities of eigenvalues of Hermitian matrices whose graph is a given tree has grown substantially and it has been led by hyper-v stopping-critical stuckWebThe 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 … hyper-v ssd configurationWeb7 de abr. de 2024 · Abstract. In this paper, we study the upper bounds for discrete Steklov eigenvalues on trees via geometric quantities. For a finite tree, we prove sharp upper … hyper-v stretched cluster