相关论文: Enumerating Chemical Graphs with Mono-block 2-Augm…

We present a general framework to generate trees every vertex of which has a non-negative weight and a color. The colors are used to impose certain restrictions on the weight and colors of other vertices. We first extend the enumeration…

Graphs are extremely versatile and ubiquitous mathematical structures with potential to model a wide range of domains. For this reason, graph problems have been of interest since the early days of computer science. Some of these problems…

A topological index reflects the physical, chemical and structural properties of a molecule, and its study has an important role in molecular topology, chemical graph theory and mathematical chemistry. It is a natural problem to…

Structural entropy is a metric that measures the amount of information embedded in graph structure data under a strategy of hierarchical abstracting. To measure the structural entropy of a dynamic graph, we need to decode the optimal…

In this paper, we develop a framework to obtain graph abstractions for decision-making by an agent where the abstractions emerge as a function of the agent's limited computational resources. We discuss the connection of the proposed…

Bispanning graphs are undirected graphs with an edge set that can be decomposed into two disjoint spanning trees. The operation of symmetrically swapping two edges between the trees, such that the result is a different pair of disjoint…

Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…

Graph-structured data arise ubiquitously in many application domains. A fundamental problem is to quantify their similarities. Graph kernels are often used for this purpose, which decompose graphs into substructures and compare these…

We investigate string graphs through the lens of graph product structure theory, which describes complicated graphs as subgraphs of strong products of simpler building blocks. A graph $G$ is called a string graph if its vertices can be…

The $k$-leaf power graph $G$ of a tree $T$ is a graph whose vertices are the leaves of $T$ and whose edges connect pairs of leaves at unweighted distance at most~$k$ in $T$. Recognition of the $k$-leaf power graphs for $k \geq 7$ is still…

In this paper, we present enumeration algorithms to list all preferred extensions of an argumentation framework. This task is equivalent to enumerating all maximal semikernels of a directed graph. For directed graphs on $n$ vertices, all…

We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross…

We enumerate graph homomorphisms to quasi-complete graphs, i.e., graphs obtained from complete graphs by removing one edge. The source graphs are complete graphs, quasi-complete graphs, cycles, paths, wheels and broken wheels. These…

Given a graph $G$, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of $G$ that belong to a certain hereditary graph class. While its optimization version, known as the minimum vertex deletion problem in…

Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…

Experimental validation of chemical processes is slow and costly, limiting exploration in materials discovery. Machine learning can prioritize promising candidates, but existing data in patents and literature is heterogeneous and difficult…

Tree structures appear in many fields of the life sciences, including phylogenetics, developmental biology and nucleic acid structures. Trees can be used to represent RNA secondary structures, which directly relate to the function of…

We describe the structure of those graphs that have largest spectral radius in the class of all connected graphs with a given degree sequence. We show that in such a graph the degree sequence is non-increasing with respect to an ordering of…

Consider the following process on a simple graph without isolated vertices: Order the edges randomly and keep an edge if and only if it contains a vertex which is not contained in some preceding edge. The resulting set of edges forms a…

Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…