Related papers: $2$-word-$\pi$-representable Graphs
In this paper, we provide a characterization of uniquely representable two-directional orthogonal ray graphs, which are defined as the intersection graphs of rightward and downward rays. The collection of these rays is called a…
Graph Convolutional Networks (GCNs) have shown strong performance in learning text representations for various tasks such as text classification, due to its expressive power in modeling graph structure data (e.g., a literature citation…
The aim of this thesis is to present an extension to the string graphs of Dixon, Duncan and Kissinger that allows the finite representation of certain infinite families of graphs and graph rewrite rules, and to demonstrate that a logic can…
Plagiarism of material from the Internet is a widespread and growing problem. Several methods used to detect the plagiarism and similarity between the source document and suspected documents such as fingerprint based on character or n-gram.…
We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition…
Pairwise compatibility graphs (PCGs) with non-negative integer edge weights recently have been used to describe rare evolutionary events and scenarios with horizontal gene transfer. Here we consider the case that vertices are separated by…
Motivated by very large-scale communication networks, we newly introduce exponentiation of graphs. Using the exponential operation on graphs, we can construct various graphs of multi-exponential order with logarithmic diameter. We show that…
Let $\Gamma$ be a finite, undirected, connected, simple graph. We say that a matching $\mathcal{M}$ is a \textit{permutable $m$-matching} if $\mathcal{M}$ contains $m$ edges and the subgroup of $\text{Aut}(\Gamma)$ that fixes the matching…
We present a framework for representing and modeling data on graphs. Based on this framework, we study three typical classes of graph signals: smooth graph signals, piecewise-constant graph signals, and piecewise-smooth graph signals. For…
We introduce the notion of a subgraph generated by an $R$-word $r$ of the Sch\"{u}tzenberger graph of a positive word $w$, $S\Gamma(w)$, where $w$ contains $r$ as its subword. We show that the word problem for a finitely presented Adian…
A graph G=(V,E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x,y) is in E for each x not equal to y. The motivation to study representable graphs came from algebra,…
This paper introduces a novel approach to learn visually grounded meaning representations of words as low-dimensional node embeddings on an underlying graph hierarchy. The lower level of the hierarchy models modality-specific word…
Continuous word representations, trained on large unlabeled corpora are useful for many natural language processing tasks. Popular models that learn such representations ignore the morphology of words, by assigning a distinct vector to each…
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
We study a geometric representation problem, where we are given a set $\cal R$ of axis-aligned rectangles with fixed dimensions and a graph with vertex set $\cal R$. The task is to place the rectangles without overlap such that two…
Graph neural networks (GNNs) have recently emerged as a dominant paradigm for machine learning with graphs. Research on GNNs has mainly focused on the family of message passing neural networks (MPNNs). Similar to the Weisfeiler-Leman (WL)…
Vector space representations of words capture many aspects of word similarity, but such methods tend to make vector spaces in which antonyms (as well as synonyms) are close to each other. We present a new signed spectral normalized graph…
We give a Python program that is capable to compute and print all the distinct trivalent 2-stratifold graphs up to $N$ white vertices with trivial fundamental group. Our algorithm uses the three basic operations to construct new graphs from…
We present an approach to enumerate graphs whose automorphism group has exactly two orbits. Our method exploits the observation that we can enumerate all graphs whose automorphism group contains a given this permutation group. We obtain the…