Related papers: On operations preserving semi-transitive orientabi…
In digital signal processing, shift-invariant filters can be represented as a polynomial expansion of a shift operation,that is, the Z-transform representation. When extended to graph signal processing (GSP), this would mean that a…
Recent work of Lazarovich provides necessary and sufficient conditions on a graph L for there to exist a unique simply-connected (k,L)-complex. The two conditions are symmetry properties of the graph, namely star-transitivity and…
Given a graph and a representation of its fundamental group, there is a naturally associated twisted adjacency operator. The main result of this article is the fact that these operators behave in a controlled way under graph covering maps.…
Partial duality generalizes the fundamental concept of the geometric dual of an embedded graph. A partial dual is obtained by forming the geometric dual with respect to only a subset of edges. While geometric duality preserves the genus of…
We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional…
In this paper we consider the separability problem for bipartite quantum states arising from graphs. Earlier it was proved that the degree criterion is the graph-theoretic counterpart of the familiar positive partial transpose criterion for…
Processing data on multiple interacting graphs is crucial for many applications, but existing approaches rely mostly on discrete filtering or first-order continuous models, dampening high frequencies and slow information propagation. In…
We investigate the structure of connected graphs, not necessarily locally finite, with infinitely many ends. On the one hand we study end-transitive such graphs and on the other hand we study such graphs with the property that the…
Graph translation is very promising research direction and has a wide range of potential real-world applications. Graph is a natural structure for representing relationship and interactions, and its translation can encode the intrinsic…
Let $S$ be a set of transpositions generating the symmetric group $S_n$. The transposition graph of $S$ is defined to be the graph with vertex set $\{1,\ldots,n\}$, and with vertices $i$ and $j$ being adjacent in $T(S)$ whenever $(i,j) \in…
Word-representable graphs, characterized by the existence of a semi-transitive orientation, form a well-studied class of graphs. Comparability graphs form another well-studied class and constitute a subclass of word-representable graphs.…
We show that every infinite, locally finite, and connected graph admitsa translation-like action by $\mathbb{Z}$, and that this action can be takento be transitive exactly when the graph has either one or two ends.The actions constructed…
We consider two operations on an edge of an embedded graph (or equivalently a ribbon graph): giving a half-twist to the edge and taking the partial dual with respect to the edge. These two operations give rise to an action of S_3^{|E(G)|},…
Graph embedding methods embed the nodes in a graph in low dimensional vector space while preserving graph topology to carry out the downstream tasks such as link prediction, node recommendation and clustering. These tasks depend on a…
A graph $G$ is primarily orientable if it is possible to orient its edges in such a way that the resulting oriented graph is prime, i.e., indecomposable under modular decomposition. We characterize primarily orientable graphs.
We present results from numerical studies of supervised learning operations in recurrent networks considered as graphs, leading from a given set of input conditions to predetermined outputs. Graphs that have optimized their output for…
Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However,…
The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of that vertex while preserving their degrees. Lov\'asz (1974)…
Graph Transformers, which incorporate self-attention and positional encoding, have recently emerged as a powerful architecture for various graph learning tasks. Despite their impressive performance, the complex non-convex interactions…
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…