Related papers: Isospectral Graph Reductions
For a given graph $G$, we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with $G$. This new specialized inverse eigenvalue problem is considered for…
Let $G$ be a group of permutations acting on an $n$-vertex set $V$, and $X$ and $Y$ be two simple graphs on $V$. We say that $X$ and $Y$ are $G$-isomorphic if $Y$ belongs to the orbit of $X$ under the action of $G$. One can naturally…
Given two graphs $G$ and $H$, we say that $G$ contains $H$ as an induced minor if a graph isomorphic to $H$ can be obtained from $G$ by a sequence of vertex deletions and edge contractions. We study the complexity of Graph Isomorphism on…
We investigate connections between the symmetries (automorphisms) of a graph and its spectral properties. Whenever a graph has a symmetry, i.e. a nontrivial automorphism $\phi$, it is possible to use $\phi$ to decompose any matrix…
Integrating data from heterogeneous sources is often modeled as merging graphs. Given two or more 'compatible', but not-isomorphic graphs, the first step is to identify a graph alignment, where a potentially partial mapping of vertices…
Two graphs $G$ and $H$ are \emph{cospectral} if the adjacency matrices share the same spectrum. Constructing cospectral non-isomorphic graphs has been studied extensively for many years and various constructions are known in the literature,…
The definition of edge-regularity in graphs is a relaxation of the definition of strong regularity, so strongly regular graphs are edge-regular and, not surprisingly, the family of edge-regular graphs is much larger and more diverse than…
Using the theory of equitable decompositions it is possible to decompose a matrix $M$ appropriately associated with a given graph. The result is a collection of smaller matrices whose collective eigenvalues are the same as the eigenvalues…
We study the complexity of the following related computational tasks concerning a fixed countable graph G: 1. Does a countable graph H provided as input have a(n induced) subgraph isomorphic to G? 2. Given a countable graph H that has a(n…
Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…
In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…
Graph isomorphism is a problem for which there is no known polynomial-time solution. Nevertheless, assessing (dis)similarity between two or more networks is a key task in many areas, such as image recognition, biology, chemistry, computer…
Large-scale graphs are widely used to represent object relationships in many real world applications. The occurrence of large-scale graphs presents significant computational challenges to process, analyze, and extract information. Graph…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
Dynamical systems on networks are inherently high-dimensional unless the number of nodes is extremely small. Dimension reduction methods for dynamical systems on networks aim to find a substantially lower-dimensional system that preserves…
Spectral characterization of graphs is an important topic in spectral graph theory, which has received a lot of attention from researchers in recent years. It is generally very hard to show a given graph to be determined by its spectrum.…
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods…
We propose a snapshots-based method to compute reduction subspaces for physics-based simulations. Our method is applicable to any mesh with some artistic prior knowledge of the solution and only requires a record of existing solutions…