vol17_pp219-233. 86KB Jun 04 2011 12:05:59 AM
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Furthermore, this representation is irreducible by Proposition 3 , and its representation graph is prime with respect to the Cartesian product since any Cartesian product graph with
In this article a fast computational method is provided in order to calculate the Moore-Penrose inverse of full rank m × n matrices and of square matrices with at least one zero row
Combinatorial matrix theory, Inertia, Inverse eigenvalue problem, Inverse inertia problem, Graph, Minimum positive semidefinite rank, Minimum rank, Nil vertex, Symmetric.. AMS
We then use the basic fact that all totally positive nonsingular square matrices are products of matrices with strictly positive diagonal entries, and all other entries zero aside
This paper surveys results in Spectral Graph Theory and the Inverse Eigenvalue Problem of a Graph, examines the connections between these problems, and presents some new results
A classic inequality for singular values of a matrixsum, including its equality case, is used to study how the energy of a graph changes when edges are removed.. One sharp bound and
Theorem 1.2. Proof of Theorem 1.1. We will use the following auxiliary results in the proof.. Let SvwT denote the graph obtained from disjoint graphs S, T by adding an edge joining
The following result gives a necessary and sufficient condition for a sign pattern to require a PLI, where we consider signings with at least one diagonal entry in {− , 0} instead
