TITLE: Can the friendship graph be determind by its adjacency spectrum?
QUESTION [5 upvotes]: Let $n\geq 1$ be an integer. The Friendship Graph (or Dutch windmill graph or $n$-Fan) $F_n$ is a graph that can be constructed by coalescence $n$ copies of the cycle graph $C_3$ with a common vertex. By construction, the friendship graph $F_n$ is isomorphic to the windmill graph $Wd\left(3,n\right)$.
Can $F_n$ be determined by its adjacency spectrum?
By the adjacency spectrum of a graph, we mean the multiset of the eigenvalues of the adjacency matrix of the graph. For a graph $G$, we denote by $Spec(G)$ its adjacency spectrum.
A graph $G$ is said to be determined by its adjacency spectrum, if $Spec(G)=Spec(H)$ for some graph $H$, then $G\cong H$. 
It is known that the friendship graph can be determined by the signless Laplacian spectrum.
See [Discrete Math. 310, No. 21, 2858-2866 (2010).]

REPLY [4 votes]: This is answered in the following recent paper:
The graphs with all but two eigenvalues equal to ±1
By Sebastian M. Cioabă, Willem H. Haemers, Jason Vermette, Wiseley Wong
One may download it from
http://arxiv.org/abs/1310.6529
The answer is no! But there is only one exception that is $F_{16}$ and all other friendship graphs can be determined by spectrum.