Related papers: Spectral properties of disordered fully-connected …
In order to obtain perfect state transfer between two sites in a network of interacting qubits, their corresponding vertices in the underlying graph must satisfy a combinatorial property called strong cospectrality. Here we determine the…
In this paper, we present some spectral sufficient conditions for a graph to be Hamilton-connected in terms of the spectral radius or signless Laplacian spectral radius of the graph. Our results improve some previous work.
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The…
Typically, graph structures are represented by one of three different matrices: the adjacency matrix, the unnormalised and the normalised graph Laplacian matrices. The spectral (eigenvalue) properties of these different matrices are…
Let $\lambda_{1}(G)$ and $\mu_{1}(G)$ denote the spectral radius and the Laplacian spectral radius of a graph $G$, respectively. Li in [Electronic J. Linear Algebra 34 (2018) 389-392] proved sharp upper bounds of $\lambda_{1}(G)$ based on…
It is reported that dynamical systems over digraphs have superior performance in terms of system damping and tolerance to time delays if the underlying graph Laplacian has a purely real spectrum. This paper investigates the topological…
The existence of Hamiltonian cycles in 1-planar graphs with higher connectivity has attracted considerable attention. Recently, the authors and Dong proved that 4-connected 1-planar chordal graphs are Hamiltonian-connected. In this paper,…
Complex optical networks containing one or more gain sections are investigated and the evidence of lasing action is reported; the emission spectrum reflects the topological disorder induced by the connections. A theoretical description well…
We study the dependence of the quantum graph Hamiltonian, its resolvent, and its spectrum on the vertex conditions and graph edge lengths. In particular, several results on the interlacing (bracketing) of the spectra of graphs with…
While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and…
We investigate a periodic quantum graph in form of a square lattice with a general self-adjoint coupling at the vertices. We analyze the spectrum, in particular, its high-energy behaviour. Depending on the coupling type, bands and gaps have…
The spectral properties of signed directed graphs, which may be naturally obtained by assigning a sign to each edge of a directed graph, have received substantially less attention than those of their undirected and/or unsigned counterparts.…
The one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators, including a distinguished, physically most…
In this paper, we study the flip graph on the perfect matchings of a complete graph of even order. We investigate its combinatorial and spectral properties including connections to the signed reversal graph and we improve a previous upper…
The spectral and localization properties of heterogeneous random graphs are determined by the resolvent distributional equations, which have so far resisted an analytic treatment. We solve analytically the resolvent equations of random…
A zero-energy mid-band singularity has been found in the energy spectrum of random matrices with correlations between diagonal and off-diagonal elements typical of vibrational problems. Two representative classes of matrices, characterizing…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
Double stranded quasiperiodic copper mean arrangement has been studied in respect of their electronic property and thermoelectric signature. The two-arm network is demonstrated by a tight binding Hamiltonian. The eigenspectrum of such…
Complex networks play a fundamental role in understanding phenomena from the collective behavior of spins, neural networks, and power grids to the spread of diseases. Topological phenomena in such networks have recently been exploited to…