The Laplacian spread of tricyclic graphs.
The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic
A graph in a certain graph class is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum among all graphs in that class. Bell et al. have identified a subclass within the connected graphs of order n and size m in which minimizing graphs belong (the complements of such graphs are either disconnected or contain a clique of size n/2 ). In this paper we discuss the minimizing graphs of a special class of graphs of order n whose complements are connected and contains...
The maximum multiplicity and the two largest multiplicities of eigenvalues in a Hermitian matrix whose graph is a tree
The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, M1, 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 focus upon M2, the maximum value of the sum of the two largest multiplicities when the largest multiplicity is M1. Upper and lower bounds are given for M2. Using a combinatorial...
The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number
In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph PKn−ω,ω among all connected graphs with n vertices and clique number ω. In addition, we show that the spectral radius μ of PKm,ω (m ≥ 1) satisfies [...] More precisely, for m > 1, μ satisfies the equation [...] where [...] and [...] . At last the spectral radius μ(PK∞,ω) of the infinite graph PK∞,ω is also discussed.
The nonexistence of rank 4 IP tensors in signature .
The Numerically Stable Reconstruction of Jacobi Matrices from Spectral Data.
The optimal perturbation bounds for the weighted Moore-Penrose inverse.
The real symmetric matrices of odd order with a P-set of maximum size
Suppose that is a real symmetric matrix of order . Denote by the nullity of . For a nonempty subset of , let be the principal submatrix of obtained from by deleting the rows and columns indexed by . When , we call a P-set of . It is known that every P-set of contains at most elements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As a first step...
The Sherman-Morrison formula and eigenvalues of a special bordered matrix.
The signless Laplacian separator of graphs.
The signless Laplacian spectral radius of graphs with given number of cut vertices
In this paper, we determine the graph with maximal signless Laplacian spectral radius among all connected graphs with fixed order and given number of cut vertices.
The Singular Values of Involutory and of Idempotent Matrices.
The singularity/nonsingularity problem for matrices satisfying diagonal dominance conditions formulated in terms of directed graphs.
The spectral gap of random graphs with given expected degrees.
The spectral radii of an operator and its modulus
The spectral radius and the maximum degree of irregular graphs.
The spectral radius of the Coxeter transformations for a generalized Cartan matrix.
The Wigner semi-circle law and the Heisenberg group
The Wigner Theorem states that the statistical distribution of the eigenvalues of a random Hermitian matrix converges to the semi-circular law as the dimension goes to infinity. It is possible to establish this result by using harmonic analysis on the Heisenberg group. In fact this convergence corresponds to the topology of the set of spherical functions associated to the action of the unitary group on the Heisenberg group.
To solving multiparameter problems of algebra. 6. Spectral characteristics of polynomial matrices.
Topological classification of linear endomorphisms
We give a classification of linear endomorphisms up to topological conjugacy.