10 papers
Doubly Stochastic Matrices and Modified Laplacian Matrices of Graphs
Enide Andrade, Geir Dahl
We consider modified Laplacian matrices of graphs, obtained by adding the identity matrix to the Laplacian matrix of a graph . This results in a positive definite matrix $…
Combinatorial Fiedler Theory and Graph Partition
Enide Andrade, Geir Dahl
Partition problems in graphs are extremely important in applications, as shown in the Data science and Machine learning literature. One approach is spectral partitioning based on a…
Sign-restricted matrices of 's, 's, and 's
Richard A. Brualdi, Geir Dahl
We study {\em sign-restricted matrices} (SRMs), a class of rectangular -matrices generalizing the alternating sign matrices (ASMs). In an SRM each partial column sum, s…
Convex -Matrices and Their Epitopes
Richard A. Brualdi, Geir Dahl
We investigate -matrices that are {\em convex}, which means that the ones are consecutive in every row and column. These matrices occur in discrete tomography. The notion of…
Diagonal Sums of Doubly Stochastic Matrices
Richard A. Brualdi, Geir Dahl
Let denote the class of doubly stochastic matrices (each such matrix is entrywise nonnegative and every row and column sum is 1). We study the diagonals of matri…
On Kemeny's constant for trees with fixed order and diameter
Lorenzo Ciardo, Geir Dahl, Steve Kirkland
Kemeny's constant of a connected graph is a measure of the expected transit time for the random walk associated with . In the current work, we consider the case when…
Permutation Matrices, Their Discrete Derivatives and Extremal Properties
Richard A. Brualdi, Geir Dahl
For a permutation , and the corresponding permutation matrix, we introduce the notion of {\em discrete derivative}, obtained by taking differences of successive entries in .…
New Bounds for the Signless Laplacian Spread
Enide Andrade, Geir Dahl, Laura Leal +1
Let be a simple graph. The signless Laplacian spread of is defined as the maximum distance of pairs of its signless Laplacian eigenvalues. This paper establishes some new b…
Alternating Sign Matrices and Hypermatrices, and a Generalization of Latin Square
Richard A. Brualdi, Geir Dahl
An alternating sign matrix, or ASM, is a -matrix where the nonzero entries in each row and column alternate in sign. We generalize this notion to hypermatrices: an $n\t…
Subdivision schemes, network flows and linear optimization
Maria Charina, Geir Dahl
We link regularity and smoothness analysis of multivariate vector subdivision schemes with network flow theory and with special linear optimization problems. This connection allows…