On eigenvalue multiplicity in signed graphs
WebIn this study we consider connected signed graphs with 2 eigenvalues that admit a vertex set partition such that the induced signed graphs also have 2 eigenvalues, each. We … Web30. nov 2024. · On eigenvalue multiplicity in signed graphs Farzaneh Ramezani 1, Peter Rowlinson 2, Zoran Stanić 3 • Institutions (3) 30 Sep 2024 - Discrete Mathematics Abstract: Given a signed graph Σ with n vertices, let μ be an eigenvalue of Σ , and let t be the codimension of the corresponding eigenspace. We prove that n ≤ t + 2 3 whenever μ ∉ 0, …
On eigenvalue multiplicity in signed graphs
Did you know?
Webexamples of signed graphs in which it is attained. We also discuss particular cases in which the bound can be decreased. Keywords: Signed graph, Eigenvalue multiplicity, Net-regular signed graph, Star complement. 2000 MSC: 05C22, 05C50 1. Introduction A signed graph Σ is a pair (G,σ), where G = (V,E) is an (unsigned) WebEnter the email address you signed up with and we'll email you a reset link.
Webeigenvalues of all connected graphs of su ciently low degree. Theorem 1.1. If G is a connected graph of maximum degree on n vertices, then the multiplicity of the second largest eigenvalue of its adjacency matrix A G is bounded by O(nlog =loglog(n)): For their application to equiangular lines, [JTY+19] only needed to show that the multiplicity of WebThe generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E …
Web04. jan 2024. · Let G be a connected graph of order n and U a unicyclic graph with the same order. We firstly give a sharp bound for mG(μ), the multiplicity of a Laplacian eigenvalue μ of G. As a straightforward result, mU(1) ⩽ n − 2. We then provide two graph operations (i.e., grafting and shifting) on graph G for which the value of mG(1) is … Web04. nov 2024. · In this study we consider connected signed graphs with 2 eigenvalues that admit a vertex set partition such that the induced signed graphs also have 2 …
Web27. sep 2024. · Graphs with high second eigenvalue multiplicity. Jiang, Tidor, Yao, Zhang, and Zhao recently showed that connected bounded degree graphs have sublinear second eigenvalue multiplicity (always referring to the adjacency matrix). This result was a key step in the solution to the problem of equiangular lines with fixed angles.
Webtheir multiplicity, form the spectrum of G˙. A characterization of signed graphs with few (here and following, distinct) eigenvalues is listed as an open problem in [1]. In particular, signed graphs with 2 eigenvalues are considered before in [5, 11, 16]. ... If is not an eigenvalue of a signed graph H (with k vertices), then there is˙ ... plant stand with copper trayWeb01. apr 2024. · The graphs with all but two eigenvalues equal to ±1. Article. Full-text available. Oct 2013. Sebastian M. Cioaba. Willem H Haemers. Jason Robert Vermette. Wiseley Wong. View. plant stand table outdoorWeb01. okt 2024. · Abstract Given a signed graph Σ with n vertices, let μ be an eigenvalue of Σ, and let t be the codimension of the corresponding eigenspace. We prove that n ≤ t + 2 … plant stand with hookWeb12. jul 2024. · Abstract We consider signed graphs with just 2 or 3 distinct eigenvalues, in particular (i) those with at least one simple eigenvalue, and (ii) those with vertex-deleted … plant stand with galvanized trayWeb01. apr 2024. · Classification of edges in a general graph associated with the change in multiplicity of an eigenvalue. K. Toyonaga, Charles R. Johnson. Mathematics. 2024. ABSTRACT We investigate the change in the multiplicities of an eigenvalue of an Hermitian matrix whose graph is a general undirected graph, when an edge is removed from the … plant stand with saucerWeb01. nov 2024. · Let T be a tree on n (≥ 7) vertices with λ as a positive eigenvalue of multiplicity k.If λ 2 ≥ 2 is an integer, then we prove that k ≤ ⌊ n − 4 3 ⌋ and all extremal … plant stand with shelfWebExamples. 1. The complete graph Kn has an adjacency matrix equal to A = J ¡ I, where J is the all-1’s matrix and I is the identity. The rank of J is 1, i.e. there is one nonzero eigenvalue equal to n (with an eigenvector 1 = (1;1;:::;1)).All the remaining eigenvalues are 0. Subtracting the identity shifts all eigenvalues by ¡1, because Ax = (J ¡ I)x = Jx ¡ x. ... plant stands for 12 pots