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Now showing items 1-10 of 11

#### 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 ...

#### On the complexity of the positive semidefinite zero forcing number

(Elsevier, 2015)

The positive semidefinite zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring and is related to a more conventional version of zero forcing. We establish a relation ...

#### On the relationship between zero forcing number and certain graph coverings

(2014)

The zero forcing number and the positive zero forcing number of a graph are
two graph parameters that arise from two types of graph colourings. The zero
forcing number is an upper bound on the minimum number of induced ...

#### The maximum nullity of a complete edge subdivision graph is equal to it zero forcing number

(International Linear Algebra Society, 2014-06)

Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of
graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is
equal to the zero forcing number for all ...

#### 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 ...

#### The enhanced principal rank characteristic sequence for skew-symmetric matrices

(Elsevier, 2015-08-15)

The enhanced principal rank characteristic sequence (epr-sequence) was originally defined for an n ×n real symmetric matrix or an n ×n Hermitian matrix. Such a sequence is defined to be l1l2···ln where lk is A,S, or N ...

#### 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 ...

#### The enhanced principal rank characteristic sequence

(Elsevier, 2015)

The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric n ×n matrix is a sequence from A,S, or N according as all, some, or none of its principal minors of order k are nonzero. Such sequences give ...