Related papers: Drawing Diestel-Leader graphs in 3D
If we parameterize the positions of all vertices of a given graph in the plane such that distances between adjacent vertices are fixed, we obtain a moving graph. An L-linkage is a realization of a moving graph in 3D-space, by representing…
In this paper we study identifying codes, locating-dominating codes, and total-dominating codes in Sierpinski graphs. We compute the minimum size of such codes in Sierpinski graphs.
In this paper, we investigate the problem of covering the vertices of a graph associated to a finite vector space as introduced by Das \cite{Das}, such that we can uniquely identify any vertex by examining the vertices that cover it. We use…
Double Toeplitz (DT) codes are codes with a generator matrix of the form $(I,T)$ with $T$ a Toeplitz matrix, that is to say constant on the diagonals parallel to the main. When $T$ is tridiagonal and symmetric we determine its spectrum…
In this paper, we give a class of reconstructible graphs.
A directed hypergraph (dihypergraph) consists of a set of vertices and a set of hyperarcs, where each hyperarc is partitioned into a head and a tail. Directed hypergraphs are useful in many applications, including the study of chemical…
Creating graph visualizations involves many decisions, such as layout, node and edge appearance, and color choices. These decisions are challenging due to the multitude of options available. For instance, graph layout can be force-directed…
We introduce L-drawings, a novel paradigm for representing directed graphs aiming at combining the readability features of orthogonal drawings with the expressive power of matrix representations. In an L-drawing, vertices have exclusive…
We describe the set of all Dirichlet forms associated to a given infinite graph in terms of Dirichlet forms on its Royden boundary. Our approach is purely analytical and uses form methods.
In this thesis, we study connections between metric and combinatorial graphs from a Dirichlet space point of view.
We classify the distance-regular Cayley graphs with least eigenvalue $-2$ and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain…
Graphs as a type of data structure have recently attracted significant attention. Representation learning of geometric graphs has achieved great success in many fields including molecular, social, and financial networks. It is natural to…
Directed acyclic graphs (DAGs) are a class of graphs commonly used in practice, with examples that include electronic circuits, Bayesian networks, and neural architectures. While many effective encoders exist for DAGs, it remains…
We introduce ProcGen3D, a new approach for 3D content creation by generating procedural graph abstractions of 3D objects, which can then be decoded into rich, complex 3D assets. Inspired by the prevalent use of procedural generators in…
Graph Transformer (GT) has recently emerged as a promising neural network architecture for learning graph-structured data. However, its global attention mechanism with quadratic complexity concerning the graph scale prevents wider…
Word-representable graphs are a subset of graphs that may be represented by a word $w$ over an alphabet composed of the vertices in the graph. In such graphs, an edge exists if and only if the occurrences of the corresponding vertices…
Generating molecular structures with desired properties is a critical task with broad applications in drug discovery and materials design. We propose 3M-Diffusion, a novel multi-modal molecular graph generation method, to generate diverse,…
We propose a heuristic method that generates a graph for order/degree problem. Target graphs of our heuristics have large order (> 4000) and diameter 3. We describe the ob- servation of smaller graphs and basic structure of our heuristics.…
A classic application of description length is for model selection with the minimum description length (MDL) principle. The focus of this paper is to extend description length for data analysis beyond simple model selection and sequences of…
We present a coded caching framework using line graphs of bipartite graphs. A clique cover of the line graph describes the uncached subfiles at users. A clique cover of the complement of the square of the line graph gives a transmission…