Related papers: Specifying Graph Languages with Type Graphs
Querying knowledge bases using ontologies is usually performed using dedicated query languages, question-answering systems, or visual query editors for Knowledge Graphs. We propose a novel approach that enables users to query the knowledge…
Grammar inference deals with determining (preferable simple) models/grammars consistent with a set of observations. There is a large body of research on grammar inference within the theory of formal languages. However, there is surprisingly…
This article describes a method to build syntactical dependencies starting from the phrase structure parsing process. The goal is to obtain all the information needed for a detailled semantical analysis. Interaction Grammars are used for…
Large Language Models (LLMs) have achieved impressive results in processing text data, which has sparked interest in applying these models beyond textual data, such as graphs. In the field of graph learning, there is a growing interest in…
Large language models (LLMs), such as GPT4 and LLaMA, are creating significant advancements in natural language processing, due to their strong text encoding/decoding ability and newly found emergent capability (e.g., reasoning). While LLMs…
We initiate a complexity theoretic study of the language based graph reachability problem (L-REACH) : Fix a language L. Given a graph whose edges are labeled with alphabet symbols of the language L and two special vertices s and t, test if…
We consider isomorphism of controllable graphs and cospectrality of distance-regularized graphs (which are known to be distance-regular or distance-biregular) in relation to logical definability. While most characterizations of these…
We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set…
These lecture notes provide an introduction to automorphism groups of graphs. Some special families of graphs are then discussed, especially the families of Cayley graphs generated by transposition sets.
We give a sharp bound for the automorphism group of a cubic simple graph with a given number of vertices. For each number of vertices we give an explicit graph attaining the bound, and prove its uniqueness in special cases.
Recent efforts leverage Large Language Models (LLMs) for modeling text-attributed graph structures in node classification tasks. These approaches describe graph structures for LLMs to understand or aggregate LLM-generated textual attribute…
Large language models (LLMs) such as GPT-4 have emerged as frontrunners, showcasing unparalleled prowess in diverse applications, including answering queries, code generation, and more. Parallelly, graph-structured data, an intrinsic data…
While advances in computing resources have made processing enormous amounts of data possible, human ability to identify patterns in such data has not scaled accordingly. Efficient computational methods for condensing and simplifying data…
A graph is $H$-free if it has no induced subgraph isomorphic to $H$. We characterize all graphs $H$ for which there are only finitely many minimal non-three-colorable $H$-free graphs. Such a characterization was previously known only in the…
Planar locally finite graphs which are almost vertex transitive are discussed. If the graph is 3-connected and has at most one end then the group of automorphisms is a planar discontinuous group and its structure is well-known. A general…
A labelling of a graph is an assignment of labels to its vertex or edge sets (or both), subject to certain conditions, a well established concept. A labelling of a graph G of order n is termed a numbering when the set of integers {1,...,n}…
We consider nonregular graphs having precisely three distinct eigenvalues. The focus is mainly on the case of graphs having two distinct valencies and our results include constructions of new examples, structure theorems, valency…
Graph plays a significant role in representing and analyzing complex relationships in real-world applications such as citation networks, social networks, and biological data. Recently, Large Language Models (LLMs), which have achieved…
Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…