Browsing Mathematics & Statistics Faculty by Author "Barrett, Wayne"
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The maximum nullity of a complete edge subdivision graph is equal to it zero forcing number
Barrett, Wayne; Butler, Steve; Catral, Minnie; Hall, Tracy; Fallat, Shaun; Hogben, Leslie; Young, Michael (International Linear Algebra Society, 201406)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 ... 
Note on NordhausGaddum problems for Colin de Verdiere type parameters
Barrett, Wayne; Fallat, Shaun; Hall, Tracy; Hogben, Leslie (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 NordhausGaddum sum lower bound is conjectured ... 
Parameters Related to TreeWidth, Zero Forcing, and Maximum Nullity of a Graph
Barioli, Francesco; Barrett, Wayne; Fallat, Shaun; Hall, Tracy; Hogben, Leslie; Shader, Bryan; van den Driessche, Pauline; van der Holst, Hein (Wiley Periodicals, Inc., 2013)Treewidth, 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
Barrett, Wayne; Butler, Steve; Catral, Minnie; Fallat, Shaun; Hall, Tracy; Hogben, Leslie; van den Driessche, Pauline; Young, Michael (Elsevier, 2014)Given an nbyn 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 ...