相关论文: The Hypergraphite: A possible extension of graphit…

It is shown that lines of adsorbed hydrogen pair atoms divide the graphene sheet into strips and form hydrogen-based superlattice structures (2HG-SL). We show that the forming of 2HG-SL drastically changes the electronic properties of…

The specific rotational alignment of two-dimensional lattices results in a moir\'e superlattice with a larger period than the original lattices and allows one to engineer the electronic band structure of such materials. So far, transport…

We characterise the structure of those graphs of a given order which maximise the number of connected induced subgraphs for seven different graph classes, each with other prescribed parameters like minimum degree, independence number,…

We provide a diagrammatic criterion for semi-adequate links to be hyperbolic. We also give a conjectural description of the satellite structures of semi-adequate links. One application of our result is that the closures of sufficiently…

One of the defining features of complex networks is the connectivity properties that we observe emerging from local interactions. Recently, hypergraphs have emerged as a versatile tool to model networks with non-dyadic, higher-order…

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…

Graphene is a famous truly two-dimensional (2D) material, possessing a cone-like energy structure near the Fermi level and treated as a gapless semiconductor. Its unique properties trigger researchers to find applications of it. The gapless…

We interpret the subgraph centrality as the partition function of a network. The entropy, the internal energy and the Helmholtz free energy are defined for networks and molecular graphs on the basis of graph spectral theory. Various…

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…

We develop a general theoretical framework based on $Z$-classification to count the number of topological bound states at a junction of chiral-symmetric one-dimensional systems. The formulation applies to general multiway junctions composed…

In recent years, the Graph Model has become increasingly popular, especially in the application domain of social networks. The model has been semantically augmented with properties and labels attached to the graph elements. It is difficult…

We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross…

Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes,…

Proposing new ways to organize carbon in 2D nanomaterials has been a relevant strategy in the search for systems with targeted properties for different applications. One focus is the study of fully sp$^2$ non-graphitic networks, with…

A graph product kernel means the kernel of the natural surjection from a graph product to the corresponding direct product. We prove that a graph product kernel of countable groups is special, and a graph product of finite or cyclic groups…

Quantum confinement endows two-dimensional (2D) layered materials with exceptional physics and novel properties compared to their bulk counterparts. Although certain two- and few-layer configurations of graphene have been realized and…

This paper presents electronic spectra of zigzag and armchair graphene nanoribbons calculated within the tight-binding model for pi-electrons. Zigzag and armchair nanoribbons of different edge geometries are considered, with surface…

Hyperbolicity is a property of a graph that may be viewed as being a "soft" version of a tree, and recent empirical and theoretical work has suggested that many graphs arising in Internet and related data applications have hyperbolic…

In this work we propose the use of a hirarchical extension of the polygonality index as a means to characterize and model geographical networks: each node is associated with the spatial position of the nodes, while the edges of the network…

By means of first-principles calculations, we predict two new types of partially hydrogenated graphene systems: C$_{6}$H$_{1}$ and C$_{6}$H$_{5}$, which are shown to be ferromagnetic (FM) semimetal and FM narrow-gap semiconductor,…