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Paper   IPM / M / 8425
School of Mathematics
  Title:   Some relations between rank of a graph and its complement
1.  S. Akbari
2.  A. Alipour
3.  E. Ghorbani (Joint with J. Ebrahimi Boroojeni and M. Mirjalalieh Shirazi)
  Status:   Published
  Journal: Linear Algebra Appl.
  Vol.:  422
  Year:  2007
  Pages:   341-347
  Supported by:  IPM
Let G be a graph of order n and rank(G) denotes the rank of its adjacency matrix. Clearly, n \leqslant rank (G) + rank G \leqslant 2n. In this paper we characterize all graphs G such that rank(G) + rank(G) = n, n + 1 or n + 2. Also for every integer n \geqslant 5 and any k, 0\leqslant k \leqslant n, we construct a graph G of order n, such that rank(G) + rank (G) = n + k.

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