Related papers: Effective masses for Laplacians on periodic graphs
In this paper, we present two new matrices, namely the resistance Laplacian and resistance signless Laplacian matrix of a connected graph. We provide a generalized form of these matrices for different classes of graphs, including the…
We show that the deficiency indices of the minimal Gaffney Laplacian on an infinite locally finite metric graph are equal to the number of finite volume graph ends. Moreover, we provide criteria, formulated in terms of finite volume graph…
We consider the Laplacian on a rooted metric tree graph with branching number $ K \geq 2 $ and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely…
Edges of bands of continuous spectrum of periodic structures arise as maxima and minima of the dispersion relation of their Floquet--Bloch transform. It is often assumed that the extrema generating the band edges are non-degenerate. This…
The critical group of a connected graph is closely related to the graph Laplacian, and is of high research value in combinatorics, algebraic geometry, statistical physics, and several other areas of mathematics. In this paper, we study the…
We consider partitions of a finite, simple, weighted graph that minimize a spectral energy functional, defined to be the maximum of the first eigenvalues on each component. These partitions are minimized with respect to a parameter that we…
We observe that the Laplacian of a random graph G on N vertices represents and explicitly solvable model in the limit of infinitely increasing N. Namely, we derive recurrent relations for the limiting averaged moments of the adjacency…
We start from a one-dimensional periodic multilayered stack in order to define a frequency power expansion of effective permittivity, permeability and bianisotropic parameters. It is shown from the first order that a simple dielectric…
Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph…
Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying…
A complex unit gain graph is a graph where each orientation of an edge is given a complex unit, which is the inverse of the complex unit assigned to the opposite orientation. We extend some fundamental concepts from spectral graph theory to…
We study the operator theory associated with such infinite graphs $G$ as occur in electrical networks, in fractals, in statistical mechanics, and even in internet search engines. Our emphasis is on the determination of spectral data for a…
Extending functions from boundary values plays an important role in various applications. In this thesis we consider discrete and continuous formulations of the problem based on $p$-Laplacians, in particular for $p=\infty$ and tight…
We investigate discrete fractional Laplacians defined on the half-lattice in several dimensions, allowing possibly different fractional orders along each coordinate direction. By expressing the half-lattice operator as a boundary…
In this note we elaborate on some notions of surface area for discrete graphs which are closely related to the inverse degree. These notions then naturally lead to associated connectivity measures of graphs and to the definition of a…
We discuss Laplacian spectrum on a finite metric graph with vertex couplings violating the time-reversal invariance. For the class of star graphs we determine, under the condition of a fixed total edge length, the configurations for which…
We introduce the weighted graph Laplacian and the notion of Schr\"odinger operator on a locally finite weighted graph. Concerning essential self-adjointness, we extend Wojciechowski's and Dodziuk's results for graphs with vertex constant…
The power graph $\mathcal{G}(G)$ of a group $G$ is a simple graph whose vertices are the elements of $G$ and two distinct vertices are adjacent if one is a power of other. In this paper, we investigate the Laplacian spectrum of the power…
In this paper we obtain several tight bounds on different types of alliance numbers of a graph: (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the…
We present a systematic collection of spectral surgery principles for the Laplacian on a metric graph with any of the usual vertex conditions (natural, Dirichlet or $\delta$-type), which show how various types of changes of a local or…