Limit points for normalized Laplacian eigenvalues.
Limit points of eigenvalues of (di)graphs
The study on limit points of eigenvalues of undirected graphs was initiated by A. J. Hoffman in 1972. Now we extend the study to digraphs. We prove: 1. Every real number is a limit point of eigenvalues of graphs. Every complex number is a limit point of eigenvalues of digraphs. 2. For a digraph , the set of limit points of eigenvalues of iterated subdivision digraphs of is the unit circle in the complex plane if and only if has a directed cycle. 3. Every limit point of eigenvalues of a set...
Line graphs: their maximum nullities and zero forcing numbers
The maximum nullity over a collection of matrices associated with a graph has been attracting the attention of numerous researchers for at least three decades. Along these lines various zero forcing parameters have been devised and utilized for bounding the maximum nullity. The maximum nullity and zero forcing number, and their positive counterparts, for general families of line graphs associated with graphs possessing a variety of specific properties are analysed. Building upon earlier work, where...
Line Graphs with Exactly two Positive Eigenvalues
Linear combinations of graph eigenvalues.
Low rank co-diagonal matrices and Ramsey graphs.
Lower bound for the norm of a vertex-transitive graph.
Lower Bounds for Estrada Index
Main eigenvalues of real symmetric matrices with application to signed graphs
An eigenvalue of a real symmetric matrix is called main if there is an associated eigenvector not orthogonal to the all-1 vector . Main eigenvalues are frequently considered in the framework of simple undirected graphs. In this study we generalize some results and then apply them to signed graphs.
Mapping directed networks.
Markov chain small-world model with asymmetric transition probabilities.
Markov product of positive definite kernels and applications to Q-matrices of graph products
We show positivity of the Q-matrix of four kinds of graph products: direct product (Cartesian product), star product, comb product, and free product. During the discussion we give an alternative simple proof of the Markov product theorem on positive definite kernels.
Matrices and graphs in Euclidean geometry.
Matrices representable by directed graphs
Matrix and discrepancy view of generalized random and quasirandom graphs
We will discuss how graph based matrices are capable to find classification of the graph vertices with small within- and between-cluster discrepancies. The structural eigenvalues together with the corresponding spectral subspaces of the normalized modularity matrix are used to find a block-structure in the graph. The notions are extended to rectangular arrays of nonnegative entries and to directed graphs. We also investigate relations between spectral properties, multiway discrepancies, and degree...
Matrix inversion and digraphs: the one factor case.
Matrix partitions with finitely many obstructions.
Maximal Canonical Graphs with Seven Nonzero Eigenvalues
Maximal Canonical Graphs with Three Negative Eigenvalues
Maximum exponent of Boolean circulant matrices with constant number of nonzero entries in their generating vector.