"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."
-- Bertrand Russell

Welcome to my Scholarship Page! Here you can find what I am currently interested in (mathematically) and a list of publications.

Summary

My research interests are in the areas of linear algebra & matrix theory and graph theory & discrete mathematics (particularly the interplay between these subjects). For example, almost any question related to the study of matrices whose entries are solely 0's and 1's can be thought of in terms of questions about graphs, and vice versa.

If G is a connected simple graph of order n, studying G then corresponds to studying the adjacency matrix A of G, where the entry in the ith row and jth column equals 1 if there is an edge between vertex i and vertex j and is equal to 0 otherwise. There is also a similar correspondence for bipartite graphs G where one independent set of vertices indexes the rows and the other indexes the columns of a matrix. With this view, much of my research has been devoted to the study of properties of matrices and graphs, especially questions which may be thought of from both perspectives.

Here is my CV (updated July 2015)

Publications

13	"Propogation time on digraphs"
	with C. Bozeman, L. Hogben, S. Butler, B. Kroschel, C. Lin, M. Catral, N. Warnberg, and M. Young
	Submitted for Publication
12	"Nearly symmetric-decomposable matrices"
	with R. A. Brualdi
	Linear and Multilinear Algebra, 63 (2015), no.7, 1468-1484
11	"Path cover number, maximum nullity, and zero forcing number of oriented graphs and other simple digraphs"
	with C. Brown, J. Carlson, N. Cox, L. Hogben, J. Hu, K. Jacobs, K. Manternach, T. Peters, N. Warnberg, and M. Young
	Involve, 8 (2015), no. 1, 147-167
10	"Minimum rank, maximum nullity, and zero forcing number of simple digraphs"
	with M. Catral, L. Hogben, M. Huynh, K. Lied, and M. Young
	Electronic Journal of Linear Algebra 26 (2013), 762-780
9	"Convertible and m-convertible matrices"
	Linear and Multilinear Algebra 60 (2012), no. 3, 267-283
8	"A Knight's Tour de Force"
	Math Horizons April 2011, 27-29
7	"Signed Domination of Graphs and (0,1)-Matrices"
	with R.A. Brualdi, L. Deaett, K. Kiernan, S. Meyer, and M. Schroeder
	Contemporary Mathematics 531 (2010), 19-42
6	"Number of forest-partitions of a graph"
	with R.A. Brualdi
	Bulletin of the ICA 60 (2010), 107-125
5	"Row and column orthogonal (0,1)-matrices"
	with R.A. Brualdi, L. Deaett, K. Kiernan and M. Schroeder
	Linear Algebra and its Applications 429 (2008), no. 11-12, 2732-2745
4	"A combinatorial proof of the Dodgson/Muir determinantal identity"
	with R.A. Brualdi
	International Journal of Information and Systems Sciences 4 (2008), no. 1, 1-7
3	"Acyclic digraphs and local hierarchy theory"
	with R.A. Brualdi, L. Deaett, and U. Bostelman
	Mathematical and Computer Modelling 45 (2007), no. 5-6, 660-667
2	"Sum list coloring graphs"
	with R.A. Brualdi, L. Deaett, and U. Bostelman
	Graphs and Combinatorics 22 (2006), no. 2, 173-183
1	Appendix to "On some degenerate deformations of commutative polynomial rings"
	M. B. Butler
	Communications in Algebra 34 (2006), no. 6, 1949-1964