Related papers: Riordan graphs II: Spectral properties
We analyze graphs attaining the extreme values of various spectral indices in the class of all simple connected graphs, as well as in the class of graphs which are not complete multipartite graphs. We also present results on density of…
In this paper we define signless Laplacian matrix of a hypergraph and obtain structural properties from its eigenvalues. We generalize several known results for graphs, relating the spectrum of this matrix with structural parameters of the…
Regular ring lattices (RRLs) are defined as peculiar undirected circulant graphs constructed from a cycle graph, wherein each node is connected to pairs of neighbors that are spaced progressively in terms of vertex degree. This kind of…
We study families of self-adjoint operators with given spectra whose sum is a scalar operator. Such families are $*$-representations of certain algebras which can be described in terms of graphs and positive functions on them. The main…
Spectral hypergraph theory has recently attracted considerable interest as it provides a natural framework for modeling higher-order relationships beyond classical graphs. In this setting, eigenvalues of adjacency, Laplacian, and…
We generalize the concept of Pascal matrices to matrices associated with sets of points by considering multidimensional binomial coefficients as entries. We study their properties and prove that the infinite matrix associated with the set…
The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic…
The $k$-token graph $F_k(G)$ of a graph $G$ is the graph whose vertices are the $k$-subsets of vertices from $G$, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in $G$. It is a known result…
Recently, Anderson et al. (2019) proposed the concept of rankability, which refers to a dataset's inherent ability to produce a meaningful ranking of its items. In the same paper, they proposed a rankability measure that is based on a…
Here we have investigated a few properties of the eigenvalues of normalized (geometric) graph Laplacian in different graphs. Preservation of eigenvalue 1 from a particular subgraph to the entire graph, the spectrum of the graph constructed…
Associative spectra of graph algebras are examined with the help of homomorphisms of DFS trees. Undirected graphs are classified according to the associative spectra of their graph algebras; there are only three distinct possibilities:…
In this article, we relate the spectrum of the discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties of the graph: the existence of a perfect matching and the existence of a Hamiltonian cycle of the…
Motivated by studies of oscillator networks, we study the spectrum of the join of several normal matrices with constant row sums. We apply our results to compute the characteristic polynomial of the join of several regular graphs. We then…
We study operators on rooted graphs with a certain spherical homogeneity. These graphs are called path commuting and allow for a decomposition of the adjacency matrix and the Laplacian into a direct sum of Jacobi matrices which reflect the…
We introduce a non-backtracking Laplace operator for graphs and we investigate its spectral properties. With the use of both theoretical and computational techniques, we show that the spectrum of this operator captures several structural…
The properties of a hypergraph explored through the spectrum of its unified matrix was made by the authors in [26]. In this paper, we introduce three different hypergraph matrices: unified Laplacian matrix, unified signless Laplacian…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
Properties of graphs that can be characterized by the spectrum of the adjacency matrix of the graph have been studied systematically recently. Motivated by the complexity of these properties, we show that there are such properties for which…