On Order and Rank of Graphs

  title={On Order and Rank of Graphs},
  author={Ebrahim Ghorbani and Ali Mohammadian and Behruz Tayfeh-Rezaie},
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. Akbari, Cameron, and Khosrovshahi conjectured that the number of vertices of every reduced graph of rank r is at most m(r) = 2 − 2 if r is even and m(r) = 5 · 2(r−3)/2 − 2 if r is… CONTINUE READING