Related papers: Seidel switching for weighted multi-digraphs and i…
In the past few decades, quantum algorithms have become a popular research area of both mathematicians and engineers. Among them, uniform mixing provides a uniform probability distribution of quantum information over time which attracts a…
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.…
We formalize the notion of a sedentary vertex and present a relaxation of the concept of a sedentary family of graphs introduced by Godsil [Linear Algebra Appl. 614:356-375, 2021]. We provide sufficient conditions for a given vertex in a…
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…
Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this…
The rise of graph analytic systems has created a need for ways to measure and compare the capabilities of these systems. Graph analytics present unique scalability difficulties. The machine learning, high performance computing, and visual…
The search for a highly discriminating and easily computable invariant to distinguish graphs remains a challenging research topic. Here we focus on cospectral graphs whose complements are also cospectral (generalized cospectral), and on…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
Entanglement is a fundamental resource for many applications in quantum information processing. Here, we investigate how quantum transport in simple quantum graphs, modeled as controlled two-level quantum systems, can be utilized to…
The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in…
We investigate the graph isomorphism (GI) in some cospectral networks. Two graph are isomorphic when they are related to each other by a relabeling of the graph vertices. We want to investigate the GI in two scalable (n + 2)-regular graphs…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
We propose a novel method using a quantum annealer -- an analog quantum computer based on the principles of quantum adiabatic evolution -- to solve the Graph Isomorphism problem, in which one has to determine whether two graphs are…
We give a new formula for computing the isospectral reduction of a matrix (and graph) down to a submatrix (or subgraph). Using this, we generalize the notion of isospectral reductions. In addition, we give a procedure for constructing a…
We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…
This paper establishes an upper bound on the number of generalized cospectral mates of simple graphs, where the generalized spectrum consists of the spectrum of a graph and its complement. Moving beyond the classical problem of identifying…
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded…
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…
A graph is a powerful concept for representation of relations between pairs of entities. Data with underlying graph structure can be found across many disciplines and there is a natural desire for understanding such data better. Deep…