Zero forcing sets and the minimum rank of graphs
Zero forcing sets and the minimum rank of graphs is a scholarly work by Leslie Hogben, Wayne W. Barrett, Steve Butler, Sebastian M. Cioaba, Dragoš Cvetković, Shaun Michael Fallat, Chris Godsil, Willem Haemers, Rana Catherine Mikkelson, Sivaram Krishnan Narayan, Olga Pryporova, Irene Sciriha, Wasin So, Dragan Stevanovic, Hein van der Holst, Kevin N. Vander Meulen, Amy Lee Wangsness Wehe, and Francesco Barioli, published in 2008 in ''Linear Algebra and its Applications''. The main subjects of the publication include mathematics, zero forcing number, zero, graph theory, graph labeling, numerical linear algebra, graph, combinatorics, discrete mathematics, rank, computation, and graph connectivity measure. The paper introduces a new graph parameter, Z(G), that is the minimum size of a zero forcing set of vertices and uses it to bound the minimum rank for numerous families of graphs, often enabling computation of the minimum rank.