Related papers: Group theoretical methods to construct the graphen…
Continuum modeling of free-standing graphene monolayer, viewed as a two dimensional 2-lattice, requires specification of the components of the shift vector that acts as an auxiliary variable. If only in-plane motions are considered the…
Let $X=(V,E)$ be a finite simple connected graph with $n$ vertices and $m$ edges. A configuration is an assignment of one of two colors, black or white, to each edge of $X.$ A move applied to a configuration is to select a black edge…
At half filling, the electronic structure of graphene can be modelled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field, an everywhere-real Kekule…
A series of carbon allotropes with novel optoelectronic and rich topological properties is predicted by systematic first-principles calculations. These fascinating carbon allotropes can be derived by inserting acetylenic linkages…
Molecular graphs generally contain subgraphs (known as groups) that are identifiable and significant in composition, functionality, geometry, etc. Flat latent representations (node embeddings or graph embeddings) fail to represent, and…
Carbon is one of the most intriguing elements in the Periodic Table. It forms many allotropes, some being known from ancient times (diamond and graphite) and some discovered ten to twenty years ago (fullerenes, nanotubes). Quite…
The linear energy dispersion of graphene electrons leads to a strongly nonlinear electromagnetic response of this material. We develop a general quantum theory of the third-order nonlinear local dynamic conductivity of graphene…
In two series of papers we construct quasi regular polyhedra and their duals which are similar to the Catalan solids. The group elements as well as the vertices of the polyhedra are represented in terms of quaternions. In the present paper…
A golden-ratio-based rectangular tiling of the first quadrant of the Euclidean plane is constructed by drawing vertical and horizontal grid lines which are located at all even powers of $\phi$ along one axis, and at all odd powers of $\phi$…
A novel crystalline structure of hybrid monolayer hexagonal boron nitride (BN) and graphene is predicted by means of the first-principles calculations. This material can be derived via boron or nitrogen atoms substituted by carbon atoms…
As a viable candidate for an all-carbon post-CMOS electronics revolution, epitaxial graphene has attracted significant attention. To realize its application potential, reliable methods for fabricating large-area single-crystalline graphene…
We report on various nanocarbons formed from a unique structural pattern containing two pentagons, three hexagons and two heptagons, resulting from local rearrange- ments around a divacancy in pristine graphene or nanotubes. This defect can…
A gain graph over a group $G$, also referred to as $G$-gain graph, is a graph where an element of a group $G$, called gain, is assigned to each oriented edge, in such a way that the inverse element is associated with the opposite…
The folding of paper, hide, and woven fabric has been used for millennia to achieve enhanced articulation, curvature, and visual appeal for intrinsically flat, two-dimensional materials. For graphene, an ideal two-dimensional material,…
A graph drawn in the plane with straight-line edges is called a geometric graph. If no path of length at most $k$ in a geometric graph $G$ is self-intersecting we call $G$ $k$-locally plane. The main result of this paper is a construction…
We show that graphene, in its simplest form and settings, is a practical table-top realization of the analog of exotic quantum gravity scenarios, which are speculated to lead to certain generalized Heisenberg algebras. In particular, we…
Graphene layers were created on both C and Si faces of semi-insulating, on-axis, 4H- and 6H-SiC substrates. The process was performed under high vacuum (<10-4 mbar) in a commercial chemical vapor deposition SiC reactor. A method for H2…
Heterogeneous graphs are present in various domains, such as social networks, recommendation systems, and biological networks. Unlike homogeneous graphs, heterogeneous graphs consist of multiple types of nodes and edges, each representing…
Higher dimensional graphs can be used to colour two-dimensional geometric graphs. If G the boundary of a three dimensional graph H for example, we can refine the interior until it is colourable with 4 colours. The later goal is achieved if…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…