Related papers: Some graph theoretical aspects of generalized trun…

The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…

In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. Towards this, we proposed the concepts of class obstruction,…

Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…

This paper surveys recent development of concepts related to coloring of signed graphs. Various approaches are presented and discussed.

Graph Neural Networks (GNN) are currently the most popular approach for learning and prediction on graph-structured data and are deployed in various fields, from social network analysis to drug discovery. However, there is limited…

We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized…

This note describes some open problems that can be examined with the purpose of gaining additional insight of how to solve the problem of finding a general classification of geodetic graphs

In a simple drawing of a graph, any two edges intersect in at most one point (either a common endpoint or a proper crossing). A simple drawing is generalized twisted if it fulfills certain rather specific constraints on how the edges are…

This short note is a supplement to [1], in which the total variation of graph distributional signals is introduced and studied. We introduce a different formulation of total variation and relate it to the notion of edge centrality. The…

Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.

We define a notion of r-generalized column distances for the j-truncation of a convolutional code. Taking the limit as j tends to infinity allows us to define r-generalized column distances of a convolutional code. We establish some…

The notions of spectral measures and spectral classes, which are well known for graphs, are generalized and investigated for oriented hypergraphs.

We raise some questions about graph polynomials, highlighting concepts and phenomena that may merit consideration in the development of a general theory. Our questions are mainly of three types: When do graph polynomials have reduction…

We present our ongoing work on understanding the limitations of graph convolutional networks (GCNs) as well as our work on generalizations of graph convolutions for representing more complex node attribute dependencies. Based on an analysis…

This tutorial review provides a guiding reference to researchers who want to have an overview of the large body of literature about graph spanners. It reviews the current literature covering various research streams about graph spanners,…

The theory of graphons has proven to be a powerful tool in many areas of graph theory. In this paper, we introduce several foundational aspects of the theory of digraphons -- asymmetric two-variable functions that arise as limits of…

Metric graphs are often introduced based on combinatorics, upon "associating" each edge of a graph with an interval; or else, casually "gluing" a collection of intervals at their endpoints in a network-like fashion. Here we propose an…

We present sweeping line graphs, a generalization of $\Theta$-graphs. We show that these graphs are spanners of the complete graph, as well as of the visibility graph when line segment constraints or polygonal obstacles are considered. Our…

The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…

We study limits of convergent sequences of string graphs, that is, graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We…