相关论文: Graph kinematics of discrete physical objects: bey…
We prove that every oriented tree on $n$ vertices with bounded maximum degree appears as a spanning subdigraph of every directed graph on $n$ vertices with minimum semidegree at least $n/2+o(n)$. This can be seen as a directed graph…
We propose an unexpected twist to description of the geometry and topology of configurations of n straight lines considered as a whole 3D entity (because the lines are inseparably linked pairwise while having linking numbers 1/2 or -1/2)…
We study the hyperbolic random geometric graph introduced in Krioukov et al. For a sequence $R_n \to \infty$, we define these graphs to have the vertex set as Poisson points distributed uniformly in balls $B(0,R_n) \subset B_d^{\alpha}$,…
We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…
We develop the theory of torsional rigidity -- a quantity routinely considered for Dirichlet Laplacians on bounded planar domains -- for Laplacians on metric graphs with at least one Dirichlet vertex. Using a variational characterization…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
Phenomenological approaches to quantum gravity try to infer model-independent laws by analyzing thought experiments and combining both quantum, relativistic, and gravitational ingredients. We first review these ingredients -three basic…
This study explores the age-old quest to construct a geometric model of a quantum particle. While static classical particle models have largely been dismissed, the focus has now shifted to intricate dynamic models that hold the promise of…
Binomial Cayley graphs are obtained by considering the binomial coefficient of the weight function of a given Cayley graph and a natural number. We introduce these objects and study two families: one associated with symmetric groups and the…
We propose a new graph metric and study its properties. In contrast to the standard distance in connected graphs, it takes into account all paths between vertices. Formally, it is defined as d(i,j)=q_{ii}+q_{jj}-q_{ij}-q_{ji}, where q_{ij}…
Simplifying graphs is a very applicable problem in numerous domains, especially in computational geometry. Given a geometric graph and a threshold, the minimum-complexity graph simplification asks for computing an alternative graph of…
It is commonly accepted that the study of 2+1 dimensional quantum gravity could teach us something about the 3+1 dimensional case. The non-perturbative methods developed in this case share, as basic ingredient, a reformulation of gravity as…
In this paper, we introduce two families of planar and self-similar graphs which have small-world properties. The constructed models are based on an iterative process where each step of a certain formulation of modules results in a final…
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link…
Graphene is a new material that exhibits remarkable properties from both fundamental and applied issues. This is a 2D matter system whose physical and mechanical features have been approached by using tight binding model, first principle…
Motivated by quantum-mechanical considerations we earlier suggested an alternative action for discretised quantum gravity which measures the perimeter of the space-time and has a dimension of length. It is the so called perimeter action,…
A factor graph of a point process is a graph whose vertices are the points of the process, and which is constructed from the process in a deterministic isometry-invariant way. We prove that the d-dimensional Poisson process has a one-ended…
Complex metrics are a double-edged sword: they allow one to replace singular spacetimes, such as those containing a big bang, with regular metrics, yet they can also describe unphysical solutions in which quantum transitions may be more…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
We initiate a systematic study of quantum properties of finite graphs, namely, quantum asymmetry, quantum symmetry, and quantum isomorphism. We define the Schmidt alternative for a class of graphs, which reveals to be a useful tool for…