Related papers: The Hypergraphite: A possible extension of graphit…

In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…

We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…

We present theoretical simulations of the electronic properties of graphene-like two-dimensional (2D) carbon networks with a periodic arrangement of defect lines formed by alternating four- and eight-membered rings. These networks can be…

We propose an explanation for the appearance of superconductivity at the interfaces of graphite with Bernal stacking order. A network of line defects with flat bands appears at the interfaces between two slightly twisted graphite…

Single layers of carbon dubbed "graphenes", from which graphite is built, have attracted broad interest in the scientific community because of recent exciting experimental results. Graphene is interesting from a fundamental research…

We consider superconducting properties of a two-dimensional Dirac material such as graphene under strain that produces a flat band spectrum in the normal state. We show that in the superconducting state, such a model results in a highly…

An exact description of $\pi$ electrons based on the tight-binding model of graphene as an alternant, plane macromolecule is presented. The model molecule can contain an arbitrary number of benzene rings and has armchair- and zigzag-shaped…

In an earlier work, finite groups whose power graphs are minimally edge connected have been classified. In this article, first we obtain a necessary and sufficient condition for an arbitrary graph to be minimally edge connected.…

We propose potential geometry for fabrication of the graphite sheets with atomically smooth edges. For such sheets with Bernal stacking, the electron-electron interaction and topology should cause sufficiently high density of states…

We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…

Superconductivity with transition temperature $T_c=1.7$ K has been reported in bilayer graphene [1,2]. The main factors, which may shed light on the mechanism of the formation of this superconductivity, are the following. Superconductivity…

Given a finite set T of maps on a finite ring R, we look at the finite simple graph G=(V,E) with vertex set V=R and edge set E={(a,b) | exists t in T, b=t(a), b not equal to a}. An example is when R=Z_n and T consists of a finite set of…

In this short note we provide a proof of boundedness of solutions for a network system composed of heterogeneous nonlinear autonomous systems interconnected over a directed graph. The sole assumptions imposed are that the systems are…

This paper studies \emph{Dirichlet arrangements}, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. We generalize descriptions of combinatorial features of graphic…

In this note, we calculate the electronic properties of a realistic atomistic model of amorphous graphene. The model contains odd membered rings, particularly five and seven membered rings and no coordination defects. We show that…

Networks are often studied as graphs, where the vertices stand for entities in the world and the edges stand for connections between them. While relatively easy to study, graphs are often inadequate for modeling real-world situations,…

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…

Associated to every state surface for a knot or link is a state graph, which embeds as a spine of the state surface. A state graph can be decomposed along cut-vertices into graphs with induced planar embeddings. Associated with each such…

Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…

We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…