Related papers: Drawing Diestel-Leader graphs in 3D

Order diagrams are an important tool to visualize the complex structure of ordered sets. Favorable drawings of order diagrams, i.e., easily readable for humans, are hard to come by, even for small ordered sets. Many attempts were made to…

We generalize the tree-confluent graphs to a broader class of graphs called Delta-confluent graphs. This class of graphs and distance-hereditary graphs, a well-known class of graphs, coincide. Some results about the visualization of…

We present IsalGraph, a method for representing the structure of any finite, simple graph as a compact string over a nine-character instruction alphabet. The encoding is executed by a small virtual machine comprising a sparse graph, a…

We show that every graph of maximum degree 3 can be represented as the intersection graph of axis parallel boxes in three dimensions, that is, every vertex can be mapped to an axis parallel box such that two boxes intersect if and only if…

In this article, we use a unified approach to prove several classes of planar graphs are DP-$3$-colorable, which extend the corresponding results on $3$-choosability.

This paper uses the theory of covering graphs to characterize some of the edge-transitive graphs which can arise as token graphs.

We describe TGView3D, an interactive 3D graph viewer optimized for exploring theory graphs. To exploit the three spatial dimensions, it extends a force-directed layout with a hierarchical component. Because of the limitations of regular…

Consider a directed graph (digraph) in which vertices are assigned color sets, and two vertices are connected if and only if they share at least one color and the tail vertex has a strictly smaller color set than the head. We seek to…

In this paper, we find strictly Deza graphs that can be obtained from the Berlekamp-van Lint-Seidel graph by applying dual Seidel switching.

This paper considers distributed storage systems (DSSs) from a graph theoretic perspective. A DSS is constructed by means of the path decomposition of a 3- regular graph into P4 paths. The paths represent the disks of the DSS and the edges…

In this paper, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets. Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks…

A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…

We prove that for every graph $G$, given fixed locations for the vertices of $G$ in $\mathbb{Z}^3$, there is a three-dimensional grid-drawing of $G$ with one bend per edge. The best previous bound was three bends per edge.

We study contact representations for graphs, which we call pixel representations in 2D and voxel representations in 3D. Our representations are based on the unit square grid whose cells we call pixels in 2D and voxels in 3D. Two pixels are…

In this note we introduce a representation of simple undirected graphs in terms of polynomials and obtain a unique code for a simple undirected graph.

Node-link diagrams are widely used to facilitate network explorations. However, when using a graph drawing technique to visualize networks, users often need to tune different algorithm-specific parameters iteratively by comparing the…

For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…

We present a construction that gives an infinite series of divisible design graphs which are Cayley graphs.

Graph code is a linear code obtained from linear codes $C$ and a certain bipartite graph G. In this paper, I propose an expansion of the definition of graph code to general $l$-partite, and give its lower bound of minimum distance. I also…

We introduce Dialz, a framework for advancing research on steering vectors for open-source LLMs, implemented in Python. Steering vectors allow users to modify activations at inference time to amplify or weaken a 'concept', e.g. honesty or…