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Paper   IPM / M / 12267
School of Mathematics
  Title:   Maximum order of trees and bipartite graphs with a given rank
1.  E. Ghrobani
2.  A. Mohammadian
3.  B. Tayfeh-Rezaie
  Status:   Published
  Journal: Discrete Mathematics
  Vol.:  312
  Year:  2012
  Pages:   3498-3501
  Supported by:  IPM
The rank of a graph is that 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 trees as well as bipartite graphs with a given rank and characterize those graphs achieving the maximum order.

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