  For any graph $G$, let $t(G)$ be the number of spanning trees of $G$, $L(G)$
be the line graph of $G$ and for any non-negative integer $r$, $S_r(G)$ be the
graph obtained from $G$ by replacing each edge $e$ by a path of length $r+1$
connecting the two ends of $e$. In this paper we obtain an expression for
$t(L(S_r(G)))$ in terms of spanning trees of $G$ by a combinatorial approach.
This result generalizes some known results on the relation between
$t(L(S_r(G)))$ and $t(G)$ and gives an explicit expression
$t(L(S_r(G)))=k^{m+s-n-1}(rk+2)^{m-n+1}t(G)$ if $G$ is of order $n+s$ and size
$m+s$ in which $s$ vertices are of degree $1$ and the others are of degree $k$.
Thus we prove a conjecture on $t(L(S_1(G)))$ for such a graph $G$.
