相关论文: Eigenvalues and Critical Groups of Adinkras

A new class of isospectral graphs is presented. These graphs are isospectral with respect to both the normalised Laplacian on the discrete graph and the standard differential Laplacian on the corresponding metric graph. The new class of…

The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral…

An ordering of colours in an Adinkra leads to an embedding of this Adinkra into a Riemann surface $X$, and a branched covering map $\beta_X:X\to\mathbb{CP}^1$. This paper shows how the dashing of edges in an Adinkra determines a signed…

This paper deals with spectral graph theory issues related to questions of monotonicity and comparison of eigenvalues. We consider finite directed graphs with non symmetric edge weights and we introduce a special self-adjoint operator as…

Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…

The traditional adjacency matrix of a mixed graph is not symmetric in general, hence its eigenvalues may be not real. To overcome this obstacle, several authors have recently defined and studied various Hermitian adjacency matrices of…

Recent efforts to classify representations of supersymmetry with no central charge have focused on supermultiplets that are aptly depicted by Adinkras, wherein every supersymmetry generator transforms each component field into precisely one…

We develop eigenvalue estimates for the Laplacians on discrete and metric graphs using different types of boundary conditions at the vertices of the metric graph. Via an explicit correspondence of the equilateral metric and discrete graph…

Let $\Gamma$ be a simple undirected graph on a finite vertex set and let $A$ be its adjacency matrix. Then $\Gamma$ is {\it singular} if $A$ is singular. The problem of characterising singular graphs is easy to state but very difficult to…

This paper consists of a few results, discovered and proved during the 2012-2013 research group at Eastern Oregon University. Inertia tables are a visual representation of the possible inertias of a given graph. The inertia of a graph…

We study the symmetry properties of the spectra of normalized Laplacians on signed graphs. We find a new machinery that generates symmetric spectra for signed graphs, which includes bipartiteness of unsigned graphs as a special case.…

Discrete amorphous materials are best described in terms of arbitrary networks which can be embedded in three dimensional space. Investigating the thermodynamic equilibrium as well as non-equilibrium behavior of such materials around second…

The spectral properties of signed directed graphs, which may be naturally obtained by assigning a sign to each edge of a directed graph, have received substantially less attention than those of their undirected and/or unsigned counterparts.…

We consider signed graphs, i.e, graphs with positive or negative signs on their edges. We construct some families of bipartite signed graphs with only two distinct eigenvalues. This leads to constructing infinite families of regular…

An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of $+1$ or $-1$. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian…

There is a deep and interesting connection between the topological properties of a graph and the behaviour of the dynamical system defined on it. We analyse various kind of graphs, with different contrasting connectivity or degree…

Eigenvalue interlacing is a versatile technique for deriving results in algebraic combinatorics. In particular, it has been successfully used for proving a number of results about the relation between the (adjacency matrix or Laplacian)…

We investigate properties of signed graphs that have few distinct eigenvalues together with a symmetric spectrum. Our main contribution is to determine all signed $(0,2)$-graphs with vertex degree at most $6$ that have precisely two…

Signed graphs are graphs whose edges get a sign $+1$ or $-1$ (the signature). Signed graphs can be studied by means of graph matrices extended to signed graphs in a natural way. Recently, the spectra of signed graphs have attracted much…

In this paper we generalise the results on eigenvalues and eigenvectors of unnormalized (combinatorial) Laplacian of two-dimensional grid presented by Edwards:2013 first to a grid graph of any dimension, and second also to other types of…