相关论文: Spectral determinant on quantum graphs
We introduce a zeta function of digraphs that determines, and is determined by, the spectra of all linear combinations of the adjacency matrix, its transpose, the out-degree matrix, and the in-degree matrix. In particular, zeta-equivalence…
Let $G$ be a simple connected undirected graph. The Laplacian spectral ratio of $G$, denoted by $R_L(G)$, is defined as the quotient between the largest and second smallest Laplacian eigenvalues of $G$, which is closely related to the…
It is now well known that ultracontractive properties of semigroups with infinitesimal generator given by an undirected graph Laplacian operator can be obtained through an understanding of the geometry of the underlying infinite weighted…
Given a connected locally finite simplicial graph $ G$ with vertex set $V$, the combinatorial Laplacian $\Delta_G \colon \R^V \to \R^V$ is defined on the space of all real-valued functions on $V$. We prove that $\Delta_G$ is surjective if…
This paper studies the Laplacian spectral characterization of some graph products. We consider a class of connected graphs: $\mathscr{G}={G : |EG|\leq|VG|+1}$, and characterize all graphs $G\in\mathscr{G}$ such that the products $G\times…
In the present article magnetic Laplacians on a graph are analyzed. We provide a complete description of the set of all operators which can be obtained from a given self-adjoint Laplacian by perturbing it by magnetic fields. In particular,…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
We develop a graph-Hilbert-space framework, inspired by non-commutative geometry, on (infinite) graphs and use it to study spectral properies of \tit{graph-Laplacians} and so-called \tit{graph-Dirac-operators}. Putting the various pieces…
In this paper, we demonstrate a useful interaction between the theory of clique partitions, edge clique covers of a graph, and the spectra of graphs. Using a clique partition and an edge clique cover of a graph we introduce the notion of a…
In the recent literature, various authors have studied spectral comparison results for Schr\"odinger operators with discrete spectrum in different settings including Euclidean domains and quantum graphs. In this note we derive such spectral…
We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph.…
A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimises the choice of wavelet for a dataset of graphs, such that their…
The power graph $P(\Omega)$ of a group $\Omega$ is a graph with the vertex set $\Omega$ such that two distinct vertices form an edge if and only if one of them is an integral power of the other. In this article, we determine the power graph…
We give the first example of a connected 4-regular graph whose Laplace operator's spectrum is a Cantor set, as well as several other computations of spectra following a common ``finite approximation'' method. These spectra are simple…
This paper introduces a novel Laplacian matrix aiming to enable the construction of spectral convolutional networks and to extend the signal processing applications for directed graphs. Our proposal is inspired by a Haar-like transformation…
We study \emph{dynamic} algorithms for maintaining spectral vertex sparsifiers of graphs with respect to a set of terminals $T$ of our choice. Such objects preserve pairwise resistances, solutions to systems of linear equations, and energy…
For a commutative ring $R$ with identity, the \emph{weakly zero-divisor graph} $W\Gamma(R)$ has vertex set $Z(R)^{\ast}$, with distinct vertices $x$ and $y$ adjacent whenever there exist nonzero $r\in{\rm Ann}(x)$ and $s\in{\rm Ann}(y)$…
The signless Laplacian spectral radius has emerged as a crucial spectral parameter in network science. This paper establishes new extremal results in spectral graph theory by investigating the signless Laplacian spectral radius ($Q$-index)…
Normalized Laplacian matrices of graphs have recently been studied in the context of quantum mechanics as density matrices of quantum systems. Of particular interest is the relationship between quantum physical properties of the density…
The spectral properties of the restricted fractional Dirichlet Laplacian in ${\sf V}$-shaped waveguides are studied. The continuous spectrum for such domains with cylindrical outlets is known to occupy the ray $[\Lambda_\dagger, +\infty)$…