The graphs with all but two eigenvalues equal to $\pm 1$
Combinatorics
2013-10-25 v1
Abstract
We determine all graphs whose adjacency matrix has at most two eigenvalues (multiplicities included) different from 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.
Cite
@article{arxiv.1310.6529,
title = {The graphs with all but two eigenvalues equal to $\pm 1$},
author = {Sebastian M. Cioabă and Willem H. Haemers and Jason Vermette and Wiseley Wong},
journal= {arXiv preprint arXiv:1310.6529},
year = {2013}
}