### Abstract

We look for the maximum order

*m(r)*of the adjacency matrix A of a graph*G*with a fixed rank*r*, provided*A*has no repeated rows or all-zero row. Akbari, Cameron and Khosrovshahi conjecture that m(r) = 2^{(r+2)/2}− 2 if*r*is even, and*m(r)*= 5 · 2^{(r−3)/2}− 2 if*r*is odd. We prove the conjecture and characterize*G*in the case that*G*contains an induced subgraph (r/2) · K2 or (r−3/2) · K2 + K3.Original language | English |
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Pages (from-to) | 223-232 |

Journal | Designs Codes and Cryptography |

Volume | 65 |

Issue number | 3 |

Publication status | Published - 2012 |