Now showing items 1-11 of 11

    • Note on Nordhaus-Gaddum 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 Nordhaus-Gaddum sum lower bound is conjectured ...
    • Parameters Related to Tree-Width, 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)
      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 ...
    • Colin de Verdiere parameters of chordal graphs 

      Mitchell, Lon; Fallat, Shaun (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 

      Fallat, Shaun; Nasserasr, Shahla (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 ...
    • Minimum number of distinct eigenvalues of graphs 

      Ahmadi, Bahman; Alinaghipour, Fatemeh; Cavers, Michael; Fallat, Shaun; Meagher, Karen; Nasserasr, Shahla (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 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 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 ...
    • On the relationship between zero forcing number and certain graph coverings 

      Alinaghipour, Fatemeh; Fallat, Shaun; Meagher, Karen (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 

      Barrett, Wayne; Butler, Steve; Catral, Minnie; Hall, Tracy; Fallat, Shaun; Hogben, Leslie; Young, Michael (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 ...
    • The enhanced principal rank characteristic sequence 

      Butler, Steve; Catral, Minnie; Fallat, Shaun; Hall, Tracy; Hogben, Leslie; van den Driessche, Pauline; Young, michael (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 ...
    • On the complexity of the positive semidefinite zero forcing number 

      Meagher, Karen; Fallat, Shaun; Yang, Boting (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 ...
    • The enhanced principal rank characteristic sequence for skew-symmetric matrices 

      Fallat, Shaun; Olesky, Dale; van den Driessche, Pauline (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 ...