... minimum rank of a graph over a field F was raisedat the 2006 American Institute of Mathematics workshop,“Spectra of Families of Matrices described by Graphs, Digraphs, and Sign Patterns,” and in ... Families of Matrices described by Graphs, Digraphs, and Sign Patterns,” and the authors thank AIM and NSF fortheir support. the electronic journal of combinatorics 15 (2008), #R25 1References[AHKLR] ... D and E are diagonal matrices, and B has pattern CS2. We claim that if A is real (respectively rational), then rank A ≥ 16 (respectively, rank A ≥ 18) the electronic journal of combinatorics...