University of Regina Department of Mathematics and Statistics |

Field of Research. **Matrix theory, directed and undirected
graphs.**

Theory and applications of nonnegative matrices, with particular emphasis on tournament matrices, algebraic connectivity for graphs and Markov chains.

Recent students.

- S. Ao, Ph.D., 1998. Thesis entitled Aspects of Chromatic Numbers and Rankings in Tournaments.

Selected Publications.

- S. Fallat, S. Kirkland and S. Pati, Minimizing algebraic connectivity over connected graphs with fixed girth, Discrete Mathematics, to appear.
- S. Kirkland, An upper bound on algebraic connectivity of graphs with many cutpoints, Electronic Journal of Linear Algebra 8 (2001), 94-109.
- S. Kirkland, and M. Neumann, Regular Markov chains for which the transition matrix has large exponent, Linear Algebra and its Applications 316 (2000), 45-65.
- S. Kirkland and S. Fallat, Perron components and algebraic connectivity for weighted graphs , Linear and Multilinear Algebra 44 (1998), 131-148.
- S. Kirkland and S. Fallat, Extremizing algebraic connectivity subject to graph theoretic constraints, Electronic Journal of Linear Algebra 3 (1998), 48-74.
- S. Kirkland, Perron vector bounds for a tournament matrix with applications to a conjecture of Brualdi and Li, Linear Algebra and its Applications 262 (1997), 209-227.
- S. Kirkland, A note on the eigenvalues of a primitive matrix with large exponent, Linear Algebra and its Applications 253 (1997), 103-112.
- S. Kirkland, M. Neumann, and B. Shader, Characteristic vertices of weighted trees via Perron values, Linear Multilinear Algebra 40 (1996), 311-325.
- S. Kirkland, On the minimum Perron value for an irreducible tournament matrix, Linear Algebra and its Applications 244 (1996), 277-304.

Editorial Work.

- Associate Editor,Electronic Journal of Linear Algebra
- Editorial Board Member, Linear and Multilinear Algebra
- Associate Editor, IMAGE - The Bulletin of the International Linear Algebra Society

Other Activities.

- Member of the Board of Directors of the International Linear Algebra Society
- Chair of the Regina Arts Commission

kirkland@math.uregina.ca