Related papers: Frames for Graph Signals on the Symmetric Group: A…

The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a…

A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…

Graph matching is an important and persistent problem in computer vision and pattern recognition for finding node-to-node correspondence between graph-structured data. However, as widely used, graph matching that incorporates pairwise…

This note provides an introduction to selected topics in algebraic graph theory, including strongly regular graphs, Steiner systems, and automorphism groups. We describe constructions and properties of notable graphs such as the Petersen…

We consider heuristic algorithm for solving graph isomorphism problem. The algorithm based on a successive splitting of the eigenvalues of the matrices which are modifications (to positive defined) of graphs' adjacency matrices.…

In the past few decades, quantum algorithms have become a popular research area of both mathematicians and engineers. Among them, uniform mixing provides a uniform probability distribution of quantum information over time which attracts a…

Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…

Data are represented as graphs in a wide range of applications, such as Computer Vision (e.g., images) and Graphics (e.g., 3D meshes), network analysis (e.g., social networks), and bio-informatics (e.g., molecules). In this context, our…

A map is a connected topological graph $\Gamma$ cellularly embedded in a surface. In this paper, applying Tutte's algebraic representation of map, new ideas for enumerating non-equivalent orientable or non-orientable maps of graph are…

We introduce and study a variant of the family of Johnson graphs, the Full-Flag Johnson graphs. We show that Full-Flag Johnson graphs are Cayley graphs on S_n generated by certain classes of permutations, and that they are in fact…

Networks with a high degree of symmetry are useful models for parallel processor networks. In earlier papers, we defined several global communication tasks (universal exchange, universal broadcast, universal summation) that can be critical…

It was proved in [Y.-Q. Feng, C. H. Li and J.-X. Zhou, Symmetric cubic graphs with solvable automorphism groups, {\em European J. Combin.} {\bf 45} (2015), 1-11] that a cubic symmetric graph with a solvable automorphism group is either a…

It has been understood that correlation functions of multi-trace operators in ${\cal N}=4$ SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand such algebras have been known to…

Frobenius algebras in the category of sets and relations ($\mathbf{Rel}$) serve as a unifying framework for various algebraic and combinatorial structures, including groupoids, effect algebras, and abstract circles. Recently, a nerve…

Let $\Gamma=(V,E)$ be a graph. If all the eigenvalues of the adjacency matrix of the graph $\Gamma$ are integers, then we say that $\Gamma$ is an integral graph. A graph $\Gamma$ is determined by its spectrum if every graph cospectral to it…

In many applications signals reside on the vertices of weighted graphs. Thus, there is the need to learn low dimensional representations for graph signals that will allow for data analysis and interpretation. Existing unsupervised…

Let C be an integral fusion category. We study some graphs, called the prime graph and the common divisor graph, related to the Frobenius-Perron dimensions of simple objects in the category C, that extend the corresponding graphs associated…

Graphs and networks play an important role in modeling and analyzing complex interconnected systems such as transportation networks, integrated circuits, power grids, citation graphs, and biological and artificial neural networks. Graph…

For an integer $n\geq 2$, let $X_n$ be the Cayley graph on the symmetric group $S_n$ generated by the set of transpositions ${(1 2),(1 3),...,(1 n)}$. It is shown that the spectrum of $X_n$ contains all integers from $-(n-1)$ to $n-1$…

This paper proposes a family of permutation-invariant graph embeddings, generalizing the Skew Spectrum of graphs of Kondor & Borgwardt (2008). Grounded in group theory and harmonic analysis, our method introduces a new class of graph…