Related papers: Connectivity for quantum graphs
This article investigates the connectivity dimension of a graph. We introduce this concept in analogy to the metric dimension of a graph, providing a graph parameter that measures the heterogeneity of the connectivity structure of a graph.…
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…
Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the…
Let $G$ be a graph on $n$ nodes. In this note, we prove that if $G$ is $(r+1)$-vertex connected, $1 \leq r \leq n-2$, then there exists a configuration $p$ in general position in $R^r$ such that the bar framework $(G,p)$ is universally…
Classical path search assumes complete graphs and scalar optimization metrics, yet real infrastructure networks are incomplete and require multi-dimensional evaluation. We introduce the concept of traversal: a generalization of paths that…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
A coarse-graining of spin networks is expressed in terms of partial tracing, thus allowing to use tools of quantum information theory. This is illustrated by the analysis of a simple black hole model, where the logarithmic correction of the…
The generalized $k$-connectivity $\kappa_k(G)$ of a graph $G$, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized…
This article summarises the current status of classical communication networks and identifies some critical open research challenges that can only be solved by leveraging quantum technologies. By now, the main goal of quantum communication…
Quantum communication demands efficient distribution of quantum entanglement across a network of connected partners. The search for efficient strategies for the entanglement distribution may be based on percolation theory, which describes…
This article delves into the concept of quantum contextuality, specifically focusing on proofs of the Kochen-Specker theorem obtained by assigning Pauli observables to hypergraph vertices satisfying a given commutation relation. The…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials,…
We introduce quantum association schemes. This allows to define distance regular and strongly regular quantum graphs. We bring examples thereof. In addition, we formulate the duality for translation quantum association schemes corresponding…
This paper proposes the definition of a quantum knot as a linear superposition of classical knots in three dimensional space. The definition is constructed and examples are discussed. Then the paper details extensions and also limitations…
We introduce a category $\mathsf{qGph}$ of quantum graphs, whose definition is motivated entirely from noncommutative geometry. For all quantum graphs $G$ and $H$ in $\mathsf{qGph}$, we then construct a quantum graph $[G,H]$ of…
We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a "contracted diameter less or equal to 2" condition, with minimal degree greater or equal to k, and some natural hypothesis on the edges connecting…
We study how quantum walks can be used to find structural anomalies in graphs via several examples. Two of our examples are based on star graphs, graphs with a single central vertex to which the other vertices, which we call external…
This is a survey of some of the consequences of the recently introduced congruences on the theory of connectednesses (radical classes) and disconnectednesses (semisimple classes) of graphs and topological spaces. In particular, it is shown…
The design of the Quantum Internet protocol stack is at its infancy and early-stage conceptualization. And different heterogeneous proposals are currently available in the literature. The underlying assumption of the existing proposals is…