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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 ...
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 ...
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 principal rank characteristic sequence over various fields
(Elsevier, 2014)
Given an n-by-n matrix, its principal rank characteristic sequence is a sequence of
length n + 1 of 0s and 1s where, for k = 0; 1,..., n, a 1 in the kth position indicates
the existence of a principal submatrix of rank ...