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  • An Erdős-Ko-Rado theorem for the derangement graph of \(PGL_3(q)\) acting on the projective plane 

    Meagher, Karen; Spiga, Pablo (SIAM J. Discrete Math. 28, 2014)
    In this paper we prove an Erdős-Ko-Rado-type theorem for intersecting sets of permutations. We show that an intersecting set of maximal size in the projective general linear group \(PGL_3(q)\), in its natural ...
  • An Erdős-Ko-Rado theorem for finite \(2\)-transitive groups 

    Meagher, Karen; Spiga, Pablo; Tiep, Pham Huu (European Journal of Combinatorics, 2016)
    We prove an analogue of the classical Erdős-Ko-Rado theorem for intersecting sets of permutations in finite \(2\)-transitive groups. Given a finite group \(G\) acting faithfully and \(2\)-transitively on the set ...
  • MIKL´ OS-MANICKAM-SINGHI CONJECTURES ON PARTIAL GEOMETRIES 

    Meagher, Karen; Ihringer, Ferdinand (2016-06)
    In this paper we give a proof of the Mikl´os-Manickam-Singhi (MMS) conjecture for some partial geometries. Specifically, we give a condition on partial geometries which implies that the MMS conjecture holds. Further, ...
  • An Erdos-Ko-Rado theorem for the derangement graph of PGL(2,q) acting on the projective plane 

    Meagher, Karen; Spiga, Pablo (SIAM Journal on Discrete Mathematics, 2014)
    Let G = PGL(2, q) be the projective general linear group acting on the projec- tive line P_q. A subset S of G is intersecting if for any pair of permutations \pi and \sigma in S, there is a projective point p in P_q such ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 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 ...
  • 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 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • A note on the fixed-point iteration for the matrix equations $X\pm A^*X^{-1}A=I$ 

    Fital, Sandra; Guo, Chun-Hua (Elsevier, 2008)
    The fixed-point iteration is a simple method for finding the maximal Hermitian positive definite solutions of the matrix equations $X\pm A^*X^{-1}A=I$ (the plus/minus equations). The convergence of this method ...
  • Detecting and solving hyperbolic quadratic eigenvalue problems 

    Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Francoise (SIAM, 2009)
    Hyperbolic quadratic matrix polynomials $Q(\lambda) = \lambda^2 A + \lambda B + C$ are an important class of Hermitian matrix polynomials with real eigenvalues, among which the overdamped quadratics are those with ...
  • Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case 

    Chiang, Chun-Yueh; Chu, Eric King-Wah; Guo, Chun-Hua; Huang, Tsung-Ming; Lin, Wen-Wei; Xu, Shu-Fang (SIAM, 2009)
    In this paper, we review two types of doubling algorithm and some techniques for analyzing them. We then use the techniques to study the doubling algorithm for three different nonlinear matrix equations in the critical ...
  • An Improved Arc Algorithm for Detecting Definite Hermitian Pairs 

    Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Francoise (SIAM, 2009)
    A 25-year old and somewhat neglected algorithm of Crawford and Moon attempts to determine whether a given Hermitian matrix pair $(A,B)$ is definite by exploring the range of the function $f(x) = x^*(A + iB)x/|x^*(A + ...
  • On Newton's method and Halley's method for the principal $p$th root of a matrix 

    Guo, Chun-Hua (Elsevier, 2010)
    If $A$ is a matrix with no negative real eigenvalues and all zero eigenvalues of $A$ are semisimple, the principal $p$th root of $A$ can be computed by Newton's method or Halley's method, with a preprocessing procedure ...

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