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.
|Place of Publication||Tilburg|
|Number of pages||7|
|Publication status||Published - 2007|
|Name||CentER Discussion Paper|
- Graph energy
- Strongly regular graph
- Hadamard matrix.