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Now showing items 1-9 of 9

#### Note on Nordhaus-Gaddum problems for Colin de Verdiere type parameters

(Public Knowledge Network, 2013)

We establish the bounds 4
on the Nordhaus-
Gaddum sum upper bound multipliers for all graphs G, in connections with certain
Colin de Verdi ere type graph parameters.
The Nordhaus-Gaddum sum lower bound is conjectured ...

#### Colin de Verdiere parameters of chordal graphs

(International Linear Algebra Society, 2013-01)

The Colin de Verdi`ere parameters mu and nu are defined to be the maximum nullity of
certain real symmetric matrices associated with a given graph. In this work, both of these parameters
are calculated for all chordal ...

#### On the null space struture associted with trees and cycles

(The Charles Babbage Research Centre, 2013-02)

In this work, we study the structure of the null spaces of matrices associated with
graphs. Our primary tool is utilizing Schur complements based on certain collections
of independent vertices. This idea is applied in ...

#### Parameters Related to Tree-Width, Zero Forcing, and Maximum Nullity of a Graph

(Wiley Periodicals, Inc., 2013)

Tree-width, and variants that restrict the allowable tree decompositions, play an important role
in the study of graph algorithms and have application to computer science. The zero forcing number is used
to study the ...

#### Minimum number of distinct eigenvalues of graphs

(International Linear Algebra Society, 2013-09)

The minimum number of distinct eigenvalues, taken over all real symmetric matrices
compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds
for q(G) are proven and then applied to ...

#### Monotone convergence of Newton-like methods for M-matrix algebraic Riccati equations

(Springer, 2013)

For the algebraic Riccati equation whose four coefficient matrices form a nonsingular $M$-matrix or an irreducible singular $M$-matrix $K$, the minimal nonnegative solution can be found by Newton's method and the doubling ...

#### On algebraic Riccati equations associated with M-matrices

(Elsevier, 2013)

We consider the algebraic Riccati equation for which the four coefficient matrices form an $M$-matrix $K$. When $K$ is a nonsingular $M$-matrix or an irreducible singular $M$-matrix, the Riccati equation is known to have ...

#### Iterative methods for a linearly perturbed algebraic matrix Riccati equation arising in stochastic control

(Taylor & Francis, 2013)

We start with a discussion of coupled algebraic Riccati equations arising in the study of
linear-quadratic optimal control problem for Markov jump linear systems. Under suitable assumptions, this system of equations has ...

#### Discernibility in the Analysis of Binary Card Sort Data

(Springer, 2013-10-11)

In an open card sorting study of 356 facial photographs, each of 25 participants created an unconstrained number of piles. We consider all 63,190 possible pairs of photos: if both photos are in the same pile for a participant, ...