Maximum order of triangle-free graphs with a given rank
  The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. We determine the maximum order of reduced triangle-free graphs with a given rank and characterize all such graphs achieving the maximum order. 
E. Ghorbani, A. Mohammadian, and B. Tayfeh-Rezaie
math.CO