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).]