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Paper   IPM / M / 13469
School of Mathematics
  Title:   Maximum order of triangle-free graphs with a given rank
  Author(s): 
1.  E. Ghorbani
2.  A. Mohammadian
3.  B. Tayfeh-Rezaie
  Status:   Published
  Journal: J. Graph Theory
  Vol.:  79
  Year:  2015
  Pages:   145-158
  Supported by:  IPM
  Abstract:
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.

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