  Let $n, d$ be integers with $1 \leq d \leq \left \lfloor \frac{n-1}{2} \right
\rfloor$, and set $h(n,d):={n-d \choose 2} + d^2$. Erd\H{o}s proved that when
$n \geq 6d$, each nonhamiltonian graph $G$ on $n$ vertices with minimum degree
$\delta(G) \geq d$ has at most $h(n,d)$ edges. He also provides a sharpness
example $H_{n,d}$ for all such pairs $n,d$. Previously, we showed a stability
version of this result: for $n$ large enough, every nonhamiltonian graph $G$ on
$n$ vertices with $\delta(G) \geq d$ and more than $h(n,d+1)$ edges is a
subgraph of $H_{n,d}$.
  In this paper, we show that not only does the graph $H_{n,d}$ maximize the
number of edges among nonhamiltonian graphs with $n$ vertices and minimum
degree at least $d$, but in fact it maximizes the number of copies of any fixed
graph $F$ when $n$ is sufficiently large in comparison with $d$ and $|F|$. We
also show a stronger stability theorem, that is, we classify all nonhamiltonian
$n$-graphs with $\delta(G) \geq d$ and more than $h(n,d+2)$ edges. We show this
by proving a more general theorem: we describe all such graphs with more than
${n-(d+2) \choose k} + (d+2){d+2 \choose k-1}$ copies of $K_k$ for any $k$.
