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We develop a picture of graphenic crystallites within disordered carbons that goes beyond the traditional model of graphitic platelets at random orientation. Using large atomistic models containing one million atoms, we redefine the meaning…
Let $\Gamma$ be the infinite cyclic group on a generator $x.$ To avoid confusion when working with $\mathbb Z$-modules which also have an additional $\mathbb Z$-action, we consider the $\mathbb Z$-action to be a $\Gamma$-action instead.…
Graphene pseudohalides are natural candidates for use in molecular sensing due to their greater chemical activity as compared to both graphene halides and pristine graphene. Though their study is still in its infancy, being hindered until…
A metric basis in a graph $G$ is a smallest possible set $S$ of vertices of $G$, with the property that any two vertices of $G$ are uniquely recognized by using a vector of distances to the vertices in $S$. A strong metric basis is a…
A \emph{mixed interval graph} is an interval graph that has, for every pair of intersecting intervals, either an arc (directed arbitrarily) or an (undirected) edge. We are particularly interested in scenarios where edges and arcs are…
The automatic analysis of chemical literature has immense potential to accelerate the discovery of new materials and drugs. Much of the critical information in patent documents and scientific articles is contained in figures, depicting the…
Let $G$ be a graph, and let $u$, $v$, and $w$ be vertices of $G$. If the distance between $u$ and $w$ does not equal the distance between $v$ and $w$, then $w$ is said to resolve $u$ and $v$. The metric dimension of $G$, denoted $\beta(G)$,…
Let $G$ be a graph with vertex set $V(G)$. For any two distinct vertices $x$ and $y$ of $G$, let $R\{x, y\}$ denote the set of vertices $z$ such that the distance from $x$ to $z$ is not equal to the distance from $y$ to $z$ in $G$. For a…
Let G be a simple graph with vertex set V(G). A subset S of V(G) is independent if no two vertices from S are adjacent. The graph G is known to be a Konig-Egervary if alpha(G) + mu(G)= |V(G)|, where alpha(G) denotes the size of a maximum…
A vertex $v \in V(G)$ is called $\lambda$-main if it belongs to a star set $X \subset V(G)$ of the eigenvalue $\lambda$ of a graph $G$ and this eigenvalue is main for the graph obtained from $G$ by deleting all the vertices in $X \setminus…
Shape graphs are complex geometrical structures commonly found in biological and anatomical systems. A shape graph is a collection of nodes, some connected by curvilinear edges with arbitrary shapes. Their high complexity stems from the…
In order to take advantage of the enormous potential of graphene for future electronic micro-circuits and other applications it is necessary to develop reliable, rapid and widely applicable methods to visualize graphene based structures. We…
Unlabeled multigraphs have diverse applications across scientific fields, from transportation and social networks to polymer physics. In particular, multigraphs are essential for studying the relationship between the spatial organization…
In this paper we consider a distance-regular graph $\Gamma$. Fix a vertex $x$ of $\Gamma$ and consider the corresponding subconstituent algebra $T$. The algebra $T$ is the $\mathbb{C}$-algebra generated by the Bose-Mesner algebra $M$ of…
The new International System of Units may let us select an integer value for Avogadro's number. Some might prefer an integer that's divisible by 12, so that an integer number of $^{12}C$ atoms may be associated (to first order) with a…
The Y-chart is a powerful tool for understanding the relationship between various views (behavioral, structural, physical) of a system, at different levels of abstraction, from high-level, architecture and circuits, to low-level, devices…
In recent years, considerable advances have been made in the study of properties of metric spaces in terms of their doubling dimension. This line of research has not only enhanced our understanding of finite metrics, but has also resulted…
Metric dimension is an essential parameter in graph theory that aids in addressing issues pertaining to information retrieval, localization, network design, and chemistry through the identification of the least possible number of elements…
In this work, we have tried to develop a detailed understanding of the physical processes occurring in those variants of Micro Pattern Gas Detectors (MPGDs) that share micro hole and micro strip geometry, like GEM, MHSP and MSGC etc. Some…
Graphene, a two-dimensional crystal made of carbon atoms, provides a new and unexpected bridge between low and high-energy physics. The field has evolved very fast and very good reviews are already available in the literature. Graphene…