Related papers: Spectra of infinite graphs: two methods of computa…
We estimate the size of the spectral gap at zero for some Hermitian block matrices. Included are quasi-definite matrices, quasi-semidefinite matrices (the closure of the set of the quasi-definite matrices) and some related block matrices…
For vertex and edge connectivity we construct infinitely many pairs of regular graphs with the same spectrum, but with different connectivity.
Differential equations are derived for a continuous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry.
We determine a lower bound for the number of edges of a 2-connected maximal nontraceable graph, and present a construction of an infinite family of maximal nontraceable graphs that realize this bound.
In this paper, we study spectra of first order properties of Erdos-Renyi random graph. We proved that minimal quantifier depth of a formula with an infinite spectrum is either 4 or 5.
We suggest three applications for the inverses: For the inverse Motzkin matrix we look at Hankel determinants, and counting the paths inside a horizontal band, and for the inverse Schr\"oder matrix we look at the paths inside the same band,…
We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an…
We use the line digraph construction to associate an orthogonal matrix with each graph. From this orthogonal matrix, we derive two further matrices. The spectrum of each of these three matrices is considered as a graph invariant. For the…
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…
We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…
We consider the problem of finding lower bounds on the I/O complexity of arbitrary computations in a two level memory hierarchy. Executions of complex computations can be formalized as an evaluation order over the underlying computation…
The two matrix model is considered, with measure given by the exponential of a sum of polynomials in two different variables. It is shown how to derive a sequence of pairs of ``dual'' finite size systems of ODEs for the corresponding…
A Neumaier graph is a non-complete edge-regular graph containing a regular clique. A Neumaier graph that is not strongly regular is called a strictly Neumaier graph. In this work we present a new construction of strictly Neumaier graphs,…
We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…
Graphs and graph transformation systems are a frequently used modelling technique for a wide range of different domains, cover- ing areas as diverse as refactorings, network topologies or reconfigurable software. Being a formal method,…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
Graph Laplacians on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of either $\delta$ or $\delta'$ type. In either case, an infinite series of trace formulae which…
During the last years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wave function statistics. In the first part of this review we give a detailed introduction to…
We study the problem of calculating noncommutative distances on graphs, using techniques from linear algebra, specifically, Birkhoff-James orthogonality. A complete characterization of the solutions is obtained in the case when the…
In this paper, we introduce a magneto-spectral invariant for finite graphs. This invariant vanishes on trees and is maximized by complete graphs. We compute this invariant for cycles, complete graphs, wheel graphs, hypercubes, complete…