Related papers: Multiset and Mixed Metric Dimension for Starphene …

Synthesizability remains a critical bottleneck in generative molecular design. While recent advances have addressed synthesizability in 2D graphs, extending these constraints to 3D for geometry-based conditional generation remains largely…

Consider a graph $\Gamma$. A set $ S $ of vertices in $\Gamma$ is called a {cyclic vertex cutset} of $\Gamma$ if $\Gamma - S$ is disconnected and has at least two components containing cycles. If $\Gamma$ has a cyclic vertex cutset, then it…

A set W \subseteq V (G) is called a resolving set, if for each pair of distinct vertices u,v \in V (G) there exists t \in W such that d(u,t) \neq d(v,t), where d(x,y) is the distance between vertices x and y. The cardinality of a minimum…

For an ordered set $W=\{w_1,w_2,...,w_k\}$ of vertices and a vertex $v$ in a connected graph $G$, the ordered $k$-vector $r(v|W):=(d(v,w_1),d(v,w_2),...,d(v,w_k))$ is called the (metric) representation of $v$ with respect to $W$, where…

We present a different way to obtain generators of metric spaces having the property that the ``position'' of every element of the space is uniquely determined by the distances from the elements of the generators. Specifically we introduce…

Crystal structure design is important for the discovery of new highly functional materials because crystal structure strongly influences material properties. Crystal structures are composed of space-filling polyhedra, which affect material…

The recent discovery of graphene has sparked significant interest, which has so far been focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particle. However, the structure of…

In a graph G, cardinality of the smallest ordered set of vertices that distinguishes every element of V (G) is the (vertex) metric dimension of G. Similarly, the cardinality of such a set is the edge metric dimension of G, if it…

Zero forcing number has recently become an interesting graph parameter studied in its own right since its introduction by the "AIM Minimum Rank -- Special Graphs Work Group", whereas metric dimension is a well-known graph parameter. We…

Graphene, the one-atom-thick sp2 hybridized carbon crystal, displays unique electronic, structural and mechanical properties, which promise a large number of interesting applications in diverse high tech fields. Many of these applications…

The family of group IV-VI monochalcogenides has an atomically puckered layered structure, and their atomic bond configuration suggests the possibility for the realization of various polymorphs. Here, we report the synthesis of the first…

Two vertices $u$ and $v$ of an undirected graph $G$ are strongly resolved by a vertex $w$ if there is a shortest path between $w$ and $u$ containing $v$ or a shortest path between $w$ and $v$ containing $u$. A vertex set $R$ is a strong…

Let $\Gamma=(V,E)$ be a finite simple graph. A matching $M \subseteq E$ is positive if there exists a weight function on $V$ such that the matching $M$ is characterized by those edges with positive weights. A positive matching decomposition…

Let C be an integral fusion category. We study some graphs, called the prime graph and the common divisor graph, related to the Frobenius-Perron dimensions of simple objects in the category C, that extend the corresponding graphs associated…

Assume that $G$ is a finite group and let $a$ and $b$ be non-negative integers. We define an undirected graph $\Gamma_{a,b}(G)$ whose vertices correspond to the elements of $G^a\cup G^b$ and in which two tuples $(x_1,\dots,x_a)$ and…

Generative models for crystalline materials often rely on equivariant graph neural networks, which capture geometric structure well but are costly to train and slow to sample. We present Crystalite, a lightweight diffusion Transformer for…

Genetic sequencing has become an increasingly affordable and accessible source of genomic data in computational biology. This data is often represented as $k$-mers, i.e., strings of some fixed length $k$ with symbols chosen from a reference…

Analysis of complex networks, particularly material networks such as the carbon skeleton of hydrocarbons generated in hydrocarbon pyrolysis in carbon-rich systems, is essential for effectively describing, modeling, and predicting their…

The metric dimension of a graph $G$ is defined as the minimum number of vertices in a subset $S\subset V(G)$ such that all other vertices are uniquely determined by their distances to the vertices in $S$, and is denoted by $\dim(G)$. In…

The understanding of the structural and thermal properties of membranes, low-dimensional flexible systems in a space of higher dimension, is pursued in many fields from string theory to chemistry and biology. The case of a two-dimensional…