### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 9 |

Volume | 2008-86 |

Publication status | Published - 2008 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2008-86 |

### Fingerprint

### Keywords

- Cayley graph
- difference set
- energy of a graph
- Hadamard matrix
- regular Hadamard matrix
- strongly regular graph
- Seidel switching.

### Cite this

*Strongly Regular Graphs with Parameters (4m4, 2m4 + m2, m4 + m2, m4 + m2) Exist for All m>1*. (CentER Discussion Paper; Vol. 2008-86). Tilburg: Operations research.

}

**Strongly Regular Graphs with Parameters (4m4, 2m4 + m2, m4 + m2, m4 + m2) Exist for All m>1.** / Haemers, W.H.; Xiang, Q.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Strongly Regular Graphs with Parameters (4m4, 2m4 + m2, m4 + m2, m4 + m2) Exist for All m>1

AU - Haemers, W.H.

AU - Xiang, Q.

N1 - Subsequently published in European Journal of Combinatorics, 2010 Pagination: 9

PY - 2008

Y1 - 2008

N2 - Using results on Hadamard difference sets, we construct regular graphical Hadamard matrices of negative type of order 4m4 for every positive integer m. If m > 1, such a Hadamard matrix is equivalent to a strongly regular graph with parameters (4m4, 2m4 +m2,m4 +m2,m4 +m2). Strongly regular graphs with these parameters have been called max energy graphs, because they have maximal energy (as defined by Gutman) among all graphs on 4m4 vertices. For odd m>3 the strongly regular graphs seem to be new.

AB - Using results on Hadamard difference sets, we construct regular graphical Hadamard matrices of negative type of order 4m4 for every positive integer m. If m > 1, such a Hadamard matrix is equivalent to a strongly regular graph with parameters (4m4, 2m4 +m2,m4 +m2,m4 +m2). Strongly regular graphs with these parameters have been called max energy graphs, because they have maximal energy (as defined by Gutman) among all graphs on 4m4 vertices. For odd m>3 the strongly regular graphs seem to be new.

KW - Cayley graph

KW - difference set

KW - energy of a graph

KW - Hadamard matrix

KW - regular Hadamard matrix

KW - strongly regular graph

KW - Seidel switching.

M3 - Discussion paper

VL - 2008-86

T3 - CentER Discussion Paper

BT - Strongly Regular Graphs with Parameters (4m4, 2m4 + m2, m4 + m2, m4 + m2) Exist for All m>1

PB - Operations research

CY - Tilburg

ER -