Related papers: From Combinatorics to Geometry: The Dynamics of Gr…
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In…
This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to use locating-dominating sets, and perform an independent…
The study of algebraic properties of groups of transformations of a manifold gives rise to an interplay between different areas of mathemathics such as topology, geometry, and dynamical systems. Especially, in this paper, we point out some…
Continuous graph neural models based on differential equations have expanded the architecture of graph neural networks (GNNs). Due to the connection between graph diffusion and message passing, diffusion-based models have been widely…
We consider diffusion on discrete measure spaces as encoded by Markovian semigroups arising from weighted graphs. We study whether the graph is uniquely determined if the diffusion is given up to order isomorphism. If the graph is recurrent…
We consider a Random Graph Model on $\mathbb{Z}^{d}$ that incorporates the interplay between the statistics of the graph and the underlying space where the vertices are located. Based on a graphical construction of the model as the…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
We connect several notions relating the structural and dynamical properties of a graph. Among them are the topological entropy coming from the vertex shift, which is related to the spectral radius of the graph's adjacency matrix, the…
The connection between contextuality and graph theory has led to many developments in the field. In particular, the sets of probability distributions in many contextuality scenarios can be described using well known convex sets from graph…
Large knowledge graphs combine human knowledge garnered from projects ranging from academia and institutions to enterprises and crowdsourcing. Within such graphs, each relationship between two nodes represents a basic fact involving these…
We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
The $k$-dominating graph $D_k(G)$ of a graph $G$ is defined on the vertex set consisting of dominating sets of $G$ with cardinality at most $k$, two such sets being adjacent if they differ by either adding or deleting a single vertex. A…
This work is devoted to the study of the relationships between graph theory and the qualitative analysis of ordinary differential equations, with a special focus on two-dimensional systems. In particular, we reinterpret classical results…
Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric…
We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…
We exploit the structure of geometric graphs on Riemannian manifolds to analyze strategic dynamic graphs at the limit, when the number of nodes tends to infinity. This framework allows to preserve intrinsic geometrical information about the…
We show how graph theory concepts can provide an insight into the origin of slow dynamics in systems with kinetic constraints. In particular, we observe that slow dynamics is related to the presence of strong hierarchies between nodes on…
A pair of graphs $(\Gamma,\Sigma)$ is called unstable if their direct product $\Gamma\times\Sigma$ admits automorphisms not from $\mathrm{Aut}(\Gamma)\times\mathrm{Aut}(\Sigma)$, and such automorphisms are said to be unexpected. The…
We show that, in discrete models of quantum gravity, emergent geometric space can be viewed as the entanglement pattern in a mixed quantum state of the "universe", characterized by a universal topological network entanglement. As a concrete…