相关论文: Spectral Properties of Matrices Associated with So…
We compute explicitly (modulo solutions of certain algebraic equations) the spectra of infinite graphs obtained by attaching one or several infinite paths to some vertices of certain finite graphs. The main result concerns a canonical form…
Given a digraph D, the complementarity spectrum of the digraph is defined as the set of complementarity eigenvalues of its adjacency matrix. This complementarity spectrum has been shown to be useful in several fields, particularly in…
A mixed graph is cospectral to its converse, with respect to the usual adjacency matrices. Hence, it is easy to see that a mixed graph whose eigenvalues occur uniquely, up to isomorphism, must be isomorphic to its converse. It is therefore…
A theory of orientation on gain graphs (voltage graphs) is developed to generalize the notion of orientation on graphs and signed graphs. Using this orientation scheme, the line graph of a gain graph is studied. For a particular family of…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to…
Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c(w,x) as well as the distributions…
On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity…
We discuss spectral properties of a charged quantum particle confined to a chain graph consisting of an infinite array of rings under influence of a magnetic field assuming a $\delta$-coupling at the points where the rings touch. We start…
We give some properties of skew spectrum of a graph, especially, we answer negatively a problem concerning the skew characteristic polynomial and matching polynomial in [M. Cavers et al., Skew-adjacency matrices of graphs, Linear Algebra…
We investigate properties of signed graphs that have few distinct eigenvalues together with a symmetric spectrum. Our main contribution is to determine all signed $(0,2)$-graphs with vertex degree at most $6$ that have precisely two…
We study the asymptotic distribution of the eigenvalues of random Hermitian periodic band matrices, focusing on the spectral edges. The eigenvalues close to the edges converge in distribution to the Airy point process if (and only if) the…
The traditional adjacency matrix of a mixed graph is not symmetric in general, hence its eigenvalues may be not real. To overcome this obstacle, several authors have recently defined and studied various Hermitian adjacency matrices of…
Spectral hypergraph theory has recently attracted considerable interest as it provides a natural framework for modeling higher-order relationships beyond classical graphs. In this setting, eigenvalues of adjacency, Laplacian, and…
We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles,…
In this paper, we aim to address the open questions raised in various recent papers regarding characterization of circulant graphs with three or four distinct eigenvalues in their spectra. Our focus is on providing characterizations and…
In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-valued coefficient of the leading term may be singular, and the…
Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using…
This paper investigates spectral properties of the deformed Laplacian matrix, which merges the Laplacian and signless Laplacian matrices of a graph through a one-parameter family of matrices. We present general results on the eigenvalues of…