### Abstract

The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Koolen and Moulton have proved that the energy of a graph on n vertices is at most n(1 + √n)/2, and that equality holds if and only if the graph is strongly regular with parameters (n, (n+√n)/2, (n+2√n)/4, (n+2√n)/4). Such graphs are equivalent to a certain type of Hadamard matrices. Here we survey constructions of these Hadamard matrices and the related strongly regular graphs.

Original language | English |
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Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 7 |

Volume | 2007-37 |

Publication status | Published - 2007 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2007-37 |

### Keywords

- Graph energy
- Strongly regular graph
- Hadamard matrix.

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## Cite this

Haemers, W. H. (2007).

*Strongly Regular Graphs with Maximal Energy*. (CentER Discussion Paper; Vol. 2007-37). Operations research.