相关论文: Enumerating Chemical Graphs with Mono-block 2-Augm…
Recursive graph queries are increasingly popular for extracting information from interconnected data found in various domains such as social networks, life sciences, and business analytics. Graph data often come with schema information that…
Graph transformation systems have the potential to be realistic models of chemistry, provided a comprehensive collection of reaction rules can be extracted from the body of chemical knowledge. A first key step for rule learning is the…
Undirected graphical models encode in a graph $G$ the dependency structure of a random vector $Y$. In many applications, it is of interest to model $Y$ given another random vector $X$ as input. We refer to the problem of estimating the…
Reverse search is a convenient method for enumerating structured objects, that can be used both to address theoretical issues and to solve data mining problems. This method has already been successfully developed to handle unordered trees.…
A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property using both artificial neural networks and mixed integer linear programming. In the framework, a…
A spanning tree of a graph $G$ is a connected acyclic spanning subgraph of $G$. We consider enumeration of spanning trees when $G$ is a $2$-tree, meaning that $G$ is obtained from one edge by iteratively adding a vertex whose neighborhood…
Graph transformation formalisms have proven to be suitable tools for the modelling of chemical reactions. They are well established in theoretical studies and increasingly also in practical applications in chemistry. The latter is made…
A new geometric background of graph invariants was introduced by Gutman, of which the simplest is the second Sombor index $SO_2$, defined as $SO_2=SO_2(G)=\sum_{uv\in E}\frac{|d^2_G(u)-d^2_G(v)|}{d^2_G(u)+d^2_G(v)}$, where $G = (V, E)$ is a…
In this article, we give two extended space formulations, respectively, for the induced tree and path polytopes of chordal graphs with vertex and edge variables. These formulations are obtained by proving that the induced tree and path…
A D2CS of a graph G is a set $S \subseteq V(G)$ with $diam(G[S]) \leq 2$. We study the problem of counting and enumerating D2CS of a graph. First we give an explicit formula for the number of D2CS in a complete k-ary tree, Fibonacci tree,…
In this paper, we propose a novel family of descriptors of chemical graphs, named cycle-configuration (CC), that can be used in the standard "two-layered (2L) model" of mol-infer, a molecular inference framework based on mixed integer…
Designing molecular structures with desired chemical properties is an essential task in drug discovery and material design. However, finding molecules with the optimized desired properties is still a challenging task due to combinatorial…
We present new short proofs of known spanning tree enumeration formulae for threshold and Ferrers graphs by showing that the Laplacian matrices of such graphs admit triangular rank-one perturbations. We then characterize the set of graphs…
A nut graph is a graph on at least 2 vertices whose adjacency matrix has nullity 1 and for which non-trivial kernel vectors do not contain a zero. Chemical graphs are connected, with maximum degree at most three. We present a new algorithm…
This paper presents the novel `uniqueness tree' algorithm, as one possible method for determining whether two finite, undirected graphs are isomorphic. We prove that the algorithm has polynomial time complexity in the worst case, and that…
Graph generation techniques are increasingly being adopted for drug discovery. Previous graph generation approaches have utilized relatively small molecular building blocks such as atoms or simple cycles, limiting their effectiveness to…
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…
An increasing 1,2-tree is a labeled graph formed by starting with a vertex and then repeatedly attaching a leaf to a vertex or a triangle to an edge, the labeling of the vertices corresponding to the order in which the vertices are added.…
Huynh, Joret, Micek, Seweryn, and Wollan (Combinatorica, 2022) introduced a graph parameter, later referred to as 2-treedepth and denoted $\mathrm{td}_2(\cdot)$. The parameter is the natural 2-connected version of treedepth. For every…
We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…