We determine all graphs whose adjacency matrix has at most two eigenvalues (multiplicities included) different from $\pm 1$ and decide which of these graphs are determined by their spectrum. This includes the so-called friendship graphs, which consist of a number of edge-disjoint triangles meeting in one vertex. It turns out that the friendship graph is determined by its spectrum, except when the number of triangles equals sixteen.
|Journal||Designs, Codes and Cryptography|
|Publication status||Published - 1 Jul 2017|
- Adjacency matrix
- Graph spectrum
- Spectral characterizations