Physical Sciences and Mathematics Commons^™

Linear Operators That Preserve Graphical Properties Of Matrices: Isolation Numbers, Leroy B. Beasley, Seok-Zun Song, Young Bae Jun

Mathematics and Statistics Faculty Publications

Let A be a Boolean {0, 1} matrix. The isolation number of A is the maximum number of ones in A such that no two are in any row or any column (that is they are independent), and no two are in a 2 × 2 submatrix of all ones. The isolation number of A is a lower bound on the Boolean rank of A. A linear operator on the set of m × n Boolean matrices is a mapping which is additive and maps the zero matrix, O, to itself. A mapping strongly preserves a set, S, if it …