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.
|Place of Publication||Tilburg|
|Number of pages||9|
|Publication status||Published - 2008|
|Name||CentER Discussion Paper|
- Cayley graph
- difference set
- energy of a graph
- Hadamard matrix
- regular Hadamard matrix
- strongly regular graph
- Seidel switching.