Abstract: The Boolean rank of a (0,1)-matrix, A, is equal to the biclique cover number of the bipartite graph whose adjacency matrix is A. There are several other numbers associated with (0,1)-matrices and graphs (undirected, directed and bipartite), such as the isolation number, the nonnegative rank, the intersection number, the dot product dimension, and the fractional versions of these, etc. In this talk we address the relationships existing among these parameters.
Biography: Professor LeRoy B. Beasley received his Ph. D. degree from the University of British Columbia in 1969. After a tour in the US Army, LeRoy taught in a high school in Idaho for nine years. In 1981 he joined the faculty at Utah State University, where he remains. His research interest at present is mostly combinatorial matrix theory, especially matrix theory pertaining to graphs. He has published in Linear Algebra (theory of permanents and Schur functions), group theory (generators of finite simple groups), as well as combinatorial matrix theory . He is known for his work on linear preservers over semirings (which includes operators on graphs, digraphs and bipartite graphs) as well as over fields.