Related papers: Drawing Diestel-Leader graphs in 3D
The representation number of a graph is the minimum number of copies of each vertex required to represent the graph as a word, such that the letters corresponding to vertices $x$ and $y$ alternate if and only if $xy$ is an edge in the…
In this paper, we present Hi-D maps, a novel method for the visualization of multi-dimensional categorical data. Our work addresses the scarcity of techniques for visualizing a large number of data-dimensions in an effective and…
A planar graph can be embedded in a piecewise linear manifold, and the lattice on each linear piece can be colored with 3-coloring. If a planar graph can be colored with multiple 3-coloring, i.e. coloring the graph in pieces with different…
We consider embeddings of 3-regular graphs into 3-dimensional Cartesian coordinates, in such a way that two vertices are adjacent if and only if two of their three coordinates are equal (that is, if they lie on an axis-parallel line) and…
This paper considers the problem of network coding for multiple unicast connections in networks represented by directed acyclic graphs. The concept of interference alignment, traditionally used in interference networks, is extended to…
In this work, we present an efficient approach for capturing sign language in 3D, introduce the 3D-LEX v1.0 dataset, and detail a method for semi-automatic annotation of phonetic properties. Our procedure integrates three motion capture…
We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of discrete Schrodinger equation that is used to write the solution for quantum graphs. Formulation of the problem and…
In this letter we present a new construction of interleavers for turbo codes from 3-regular Hamiltonian graphs. The interleavers can be generated using a few parameters, which can be selected in such a way that the girth of the interleaver…
We survey some of the known results on eigenvalues of Cayley graphs and their applications, together with related results on eigenvalues of Cayley digraphs and generalizations of Cayley graphs.
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
There is a well-documented research programme on graph operators which addresses questions such as `Which graphs appear as images of graphs?'; `Which graphs are fixed under the operator?'; `What happens if the operator is iterated?' In this…
Highly-regular graphs can be regarded as a combinatorial generalization of distance-regular graphs. From this standpoint, we study combinatorial aspects of highly-regular graphs. As a result, we give the following three main results in this…
We introduce the idea of temporal graphs, a representation that encodes temporal data into graphs while fully retaining the temporal information of the original data. This representation lets us explore the dynamic temporal properties of…
Although there exist several libraries for deep learning on graphs, they are aiming at implementing basic operations for graph deep learning. In the research community, implementing and benchmarking various advanced tasks are still painful…
There has been a recent surge in learning generative models for graphs. While impressive progress has been made on static graphs, work on generative modeling of temporal graphs is at a nascent stage with significant scope for improvement.…
Motivated by a problem in computer architecture we introduce a notion of the perfect distance-dominating set, PDDS, in a graph. PDDSs constitute a generalization of perfect Lee codes, diameter perfect codes, as well as other codes and…
Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for…
Train timetables can be represented as event graphs, where correspond to a train passing through a location at a certain point in time. A visual representation of an event graph is important for many applications such as dispatching and…
An encoding of directed acyclic graphs (DAGs) on labeled vertices is proposed, which is a generalisation of the Pr\"ufer code for labeled trees, if a certain orienation on the edges of the tree is introduced. Hence it is shown that the…
We classify and construct all line graphs that are $3$-polytopes (planar and $3$-connected). Apart from a few special cases, they are all obtained starting from the medial graphs of cubic (i.e., $3$-regular) $3$-polytopes, by applying two…