Related papers: Some graph theoretical aspects of generalized trun…
We examine the chromatic index of generalized truncations of graphs and multigraphs.
Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs. In this paper we introduce the concept of proper thinness, such that graphs with bounded proper thinness generalize proper interval graphs. We study…
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.
In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…
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…
Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…
The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is…
The vertices of a $k$-token graph of a graph $G$ correspond to $k$ indistinguishable tokens placed on $k$ different vertices of $G$. Changing some conditions on both the nature of the tokens and the number of tokens allowed in each vertex…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
We propose a new approach for defining and searching clusters in graphs that represent real technological or transaction networks. In contrast to the standard way of finding dense parts of a graph, we concentrate on the structure of edges…
A mixed graph can be seen as a type of digraph containing some edges (two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line digraphs. These structures…
In this paper, we introduce a generalized concept of vertex transitivity in graphs called generalized vertex transitivity. We put forward a new invariant called transitivity number of a graph. The value of this invariant in different…
The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an…
We introduce the concept of distance ideals of graphs, which can be regarded as a generalization of the Smith normal form and the spectra of the distance matrix of a graph. We obtain a classification of the graphs with at most one trivial…
Analytics on large-scale graphs have posed significant challenges to computational efficiency and resource requirements. Recently, Graph condensation (GC) has emerged as a solution to address challenges arising from the escalating volume of…
Despite the celebrated popularity of Graph Neural Networks (GNNs) across numerous applications, the ability of GNNs to generalize remains less explored. In this work, we propose to study the generalization of GNNs through a novel…
Many real-world datasets can be naturally represented as graphs, spanning a wide range of domains. However, the increasing complexity and size of graph datasets present significant challenges for analysis and computation. In response, graph…
The thinness of a graph is a width parameter that generalizes some properties of interval graphs, which are exactly the graphs of thinness one. Many NP-complete problems can be solved in polynomial time for graphs with bounded thinness,…
A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…