On the multiplicities of graph eigenvalues
Web1 de abr. de 2008 · We study the maximum possible multiplicity of an eigenvalue of a matrix whose graph is a tree, expressing that maximum multiplicity in terms of certain parameters associated with the tree. 151 Highly Influential View 11 excerpts, references methods and background Algebraic combinatorics C. Godsil Mathematics Chapman and Hall … WebDownloadable (with restrictions)! For a connected graph G, let e(G) be the number of its distinct eigenvalues and d be the diameter. It is well known that e(G)≥d+1. This shows η≤n−d, where η and n denote the nullity and the order of G, respectively. A graph is called minimal if e(G)=d+1. In this paper, we characterize all trees satisfying η(T)=n−d or n−d−1.
On the multiplicities of graph eigenvalues
Did you know?
WebThis book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees … WebEigenvalues, Multiplicities and Graphs - February 2024. Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better …
Web1 de mai. de 2024 · In this paper we investigate the relation between eigenvalue distribution and graph structure of two classes of graphs: the ( m, k) -stars and l-dependent graphs. We give conditions on the topology and edge weights in order to get values and multiplicities of Laplacian matrix eigenvalues. We prove that a vertex set reduction on … Webof a graph directly from the eigenvalues of its self-loop graphs GS and the eigenvalues of GV (G)\S. Indeed, if we have λ 1(GS) and λn(GV (G)\S), we can determine whether G is bipartite. Another immediate consequence of Theorem 3.3 is the following corollary. Corollary 3.5. [13, Theorem 3] Let G be a bipartite graph of order n with vertex set ...
Web8 de fev. de 2015 · Given a simple graph G, let A(G) be its adjacency matrix. A principal submatrix of A(G) of order one less than the order of G is the adjacency matrix of its vertex deleted subgraph. It is well-known that the multiplicity of any eigenvalue of A(G) and such a principal submatrix can differ by at most one. Therefore, a vertex v of G is a downer … Web1 de jul. de 2005 · Mathematics Graphs A note on the multiplicities of the eigenvalues of a graph Authors: Carlos M. da Fonseca Kuwait College of Science and Technology …
Web1 de nov. de 2024 · The theory of star complement is widely used to study the multiplicities of graph eigenvalues, such as for trees and for graphs that are regular, cubic, quartic, …
Web1 de fev. de 2014 · The energy of a graph is defined as the sum of absolute values of the eigenvalues. A graph G on n vertices is said to be borderenergetic if its energy equals … bip meaning schoolWebThis book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the … bip medicaidWeb19 de nov. de 2024 · Title: Forbidden induced subgraphs for graphs and signed graphs with eigenvalues bounded from below. Authors: Zilin Jiang, ... \in \{1,\sqrt2,\sqrt3\}$, and they proposed a conjecture on the limit in terms of eigenvalue multiplicities of signed graphs. We establish their conjecture whenever $(1-\alpha)/(\alpha - \beta) ... bip min finWeb12 de mai. de 2003 · ON THE MULTIPLICITIES OF GRAPH EIGENVALUES Bulletin of the London Mathematical Society Cambridge Core ON THE MULTIPLICITIES OF … da-lite locking switch cover plateWeb1 de fev. de 2014 · On the multiplicity of positive eigenvalues of a graph Fenglei Tian, Yiju Wang Mathematics Linear Algebra and its Applications 2024 2 Save Alert A note on the … da lite low voltage switchWeb15 de mai. de 2024 · For a graph G, let σ ( G) be the set consisting of all distinct eigenvalues of its adjacency matrix. If μ ∈ σ ( G) is an eigenvalue of G, we denote its multiplicity by m ( μ). In particular, the multiplicity of 0 is denoted by η ( G) ( = m ( 0) ). The rank r ( G) of G is the rank of its adjacency matrix. Thus r ( G) + η ( G) = n. da lite no 6 wall bracketWebThis article mainly studies first-order coherence related to the robustness of the triplex MASs consensus models with partial complete graph structures; the performance index is studied through algebraic graph theory. The topologies of the novel triplex networks are generated by graph operations and the approach of graph spectra is applied to calculate the first … da lite motorized screen wiring diagram