  The $(k,r)$-fan is the graph consisting of $k$ copies of the complete graph
$K_r$ which intersect in a single vertex, and is denoted by $F_{k,r}$.
Erd\H{o}s, F\"uredi, Gould and Gunderson [J. Combin. Theory Ser. B 64 (1995)
89--100] determined the maximum number of edges in an $n$-vertex graph that
does not contain $F_{k,3}$ as a subgraph. Furthermore, Chen, Gould, Pfender and
Wei [J. Combin. Theory Ser. B 89 (2003) 159--171] proved the analogous result
on $F_{k,r}$ for the general case $r\ge 3$.In this paper, we show that for
sufficiently large $n$, the graphs of order $n$ that contain no copy of
$F_{k,r}$ and attain the maximum spectral radius are also edge-extremal. That
is, such graphs must have $\mathrm{ex}(n, F_{k,r})$ edges.
