Related papers: Group theoretical methods to construct the graphen…
In this paper, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets. Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks…
The paper describes a construction of abstract polytopes from Cayley graphs of symmetric groups. Given any connected graph G with p vertices and q edges, we associate with G a Cayley graph of the symmetric group S_p and then construct a…
Consider a graphed holomorphic surface $u=F(x,y)$ in $\mathbb{C}^3_{x,y,u}$ under the action of the affine transformation group $A(3)$. In 1999, Eastwood and Ezhov obtained a list of homogeneous models by determining possible tangential…
Electron transport in graphene is along the sheet but junction devices are often made by stacking different sheets together in a "side-contact" geometry which causes the current to flow perpendicular to the sheets within the device. Such…
Untangling is a process in which some vertices of a planar graph are moved to obtain a straight-line plane drawing. The aim is to move as few vertices as possible. We present an algorithm that untangles the cycle graph C_n while keeping at…
Graphene is at the centre of an ever growing research effort due to its unique properties, interesting for both fundamental science and applications. A key requirement for applications is the development of industrial-scale, reliable,…
The hierarchical graphene model is a simple toy model which is useful to understand the mechanics of renormalization group flows in super-renormalizable systems. It is based on a model of interacting electrons in graphene, for which the…
Periodic tilings play a role in the decorative arts, in construction and in crystal structures. Combinatorial tiling theory allows the systematic generation, visualization and exploration of such tilings of the plane, sphere and hyperbolic…
We formulate the theory of a 2-form gauge field on a Euclidean spacetime lattice. In this approach, the fundamental degrees of freedom live on the faces of the lattice, and the action can be constructed from the sum over Wilson surfaces…
Let G be a graph. The (unlabeled) configuration space of n points on G is the space of all n-element subsets of G. The fundamental group of such a configuration space is called a graph braid group. We use a version of discrete Morse theory…
A conformal field theory (CFT) is a quantum field theory which is invariant under conformal transformations; a group action that preserve angles but not necessarily lengths. There are two traditional approaches to the construction of CFTs:…
In this work we shed light on the early stage of the chemical vapor deposition of graphene on Ge(001) surfaces. By a combined use of microRaman and x-ray photoelectron spectroscopies, and scanning tunneling microscopy and spectroscopy, we…
Graphane is a two-dimensional system consisting of a single layer of fully saturated (sp$^3$ hybridization) carbon atoms. In an ideal graphane structure C-H bonds exhibit an alternating pattern (up and down with relation to the plane…
We describe a method to classify crystallographic tilings of the Euclidean and hyperbolic planes by tiles whose stabiliser group contains translation isometries or whose topology is not that of a closed disk. We tackle this problem from two…
This review on graphene, a one atom thick, two-dimensional sheet of carbon atoms, starts with a general description of the graphene electronic structure as well as a basic experimental toolkit for identifying and handling this material.…
The spatial distributions of the valence-electron density and the total energy reliefs for water (or methanol) migration on the free surface of graphene are obtained, by using the electron density functional and ab initio pseudopotential…
Let $C_{k_1}, \ldots, C_{k_n}$ be cycles with $k_i\geq 2$ vertices ($1\le i\le n$). By attaching these $n$ cycles together in a linear order, we obtain a graph called a polygon chain. By attaching these $n$ cycles together in a cyclic…
The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^2bc$ are classified as $3$ classes: a sequence of two-parameter families of $2$-layer earth map tilings with $2n$ $(n\ge3)$ tiles, a one-parameter family of…
In this work methods of construction of cubic graphs are analyzed and a theorem of existence of a colored disc traversing each pair of linked edges belonging to an elementary cycle of a planar cubic graph is proved.
Graphene, a single atomic layer of graphitic carbon, has attracted intense attention due to its extraordinary properties that make it a suitable material for a wide range of technological applications. Large-area graphene films, which are…