Related papers: Graph-theoretic perspective on a special class of …
Graph theory is a branch of mathematics in which pair-wise relations between objects are studied. My PhD thesis, supervised by David R. Wood, introduces and investigates a new family of graphs, called link graphs, that generalises the…
Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…
Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic,…
We survey work on coloring, list coloring, and painting squares of graphs; in particular, we consider strong edge-coloring. We focus primarily on planar graphs and other sparse classes of graphs.
We study topological properties of the graph topology.
Graph Neural Networks (GNNs) are learning models aimed at processing graphs and signals on graphs. The most popular and successful GNNs are based on message passing schemes. Such schemes inherently have limited expressive power when it…
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…
In this paper new Steiner systems $S(2,6,111)$, $S(2,6,121)$, $S(2,6,126)$, $S(2,7,169)$, $S(2,7,175)$ and possibly others with point-transitive (commutative except $S(2,6,111)$ case) automorphism groups are introduced.
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
One of the most famous applications of Graph Theory is in the field of Channel Assignment Problems. There are varieties of graph colouring concepts that are used for different requirements of frequency assignments in communication channels.…
A $t$-tone coloring of a graph $G$ assigns to each vertex a set of $t$ colors such that any pair of vertices $u, v$ with distance $d$ can share at most $d-1$ colors. In this note, we prove several new results on $t$-tone coloring. For…
Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory…
The demand of two-dimensional source coding and constrained coding has been getting higher these days, but compared to the one-dimensional case, many problems have remained open as the analysis is cumbersome. A main reason for that would be…
A graph is 1-planar if it can be drawn on a plane so that each edge is crossed by at most one other edge. In this paper, we first give a useful structural theorem for 1-planar graphs, and then apply it to the list edge and list total…
We propose a new approach to text semantic analysis and general corpus analysis using, as termed in this article, a "bi-gram graph" representation of a corpus. The different attributes derived from graph theory are measured and analyzed as…
We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.
A $t$-tone $k$-coloring of a graph $G$ assigns a set of $t$ distinct colors from $\{1, \dots, k\}$ to each vertex so that vertices at distance $d$ share fewer than $d$ common colors. The $t$-tone chromatic number of $G$ is the minimum $k$…
It is a classical problem in algebraic topology asked by Steenrod which graded rings occur as the cohomology ring of a space. In this paper, we define an algebraic version of the graph colouring, span colouring, and observe the relation…
The class of Euclidean unit disk graphs is one of the most fundamental and well-studied graph classes with underlying geometry. In this paper, we identify this class as a special case in the broader class of hyperbolic unit disk graphs and…
Graphs and hypergraphs are foundational structures in discrete mathematics. They have many practical applications, including the rapidly developing field of bioinformatics, and more generally, biomathematics. They are also a source of…