Related papers: Symmetric Graphs and their Quotients
Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines…
In this paper we consider the communication problem that involves transmission of correlated sources over broadcast channels. We consider a graph-based framework for this information transmission problem. The system involves a source coding…
We consider the problem of computing identifying codes of graphs and its fractional relaxation. The ratio between the size of optimal integer and fractional solutions is between 1 and 2 ln(|V|)+1 where V is the set of vertices of the graph.…
Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
In this note, we study non-transitive graphs and prove a number of results when they satisfy a coarse version of transitivity. Also, for each finitely generated group $G$, we produce continuum many pairwise non-quasi-isometric regular…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
There are many variations on partition functions for graph homomorphisms or colorings. The case considered here is a counting or hard constraint problem in which the range or color graph carries a free and vertex transitive Abelian group…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
Graphs are widely used to model execution dependencies in applications. In particular, the NP-complete problem of partitioning a graph under constraints receives enormous attention by researchers because of its applicability in…
Recursive graph queries are increasingly popular for extracting information from interconnected data found in various domains such as social networks, life sciences, and business analytics. Graph data often come with schema information that…
The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. We introduce commutatively closed graphs and investigate properties of commutatively…
Fiol has characterized quotient-polynomial graphs as precisely the connected graphs whose adjacency matrix generates the adjacency algebra of a symmetric association scheme. We show that a collection of non-negative integer parameters of…
The problem of extending partial geometric graph representations such as plane graphs has received considerable attention in recent years. In particular, given a graph $G$, a connected subgraph $H$ of $G$ and a drawing $\mathcal{H}$ of $H$,…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
The partial representation extension problem generalizes the recognition problem for classes of graphs defined in terms of vertex representations. We exhibit circular-arc graphs as the first example of a graph class where the recognition is…
In the branch of mathematics known as graph theory, graphs are considered as a set of points, called vertices, with connections between these points, called edges. The purpose of this paper is to study mappings between two graphs that have…
The spectral excess theorem for distance-regular graphs states that a regular (connected) graph is distance-regular if and only if its spectral-excess equals its average excess. A bipartite graph is distance-biregular when it is…
For a derived stack obtained as a quotient of a derived affine scheme by a reductive group, we show that shifted symplectic structures can be characterized by the Cartan-de Rham complex. For non-reductive groups, we also show the analogous…