  In this paper we find asymptotic enumerations for the number of line graphs
on $n$-labelled vertices and for different types of related combinatorial
objects called 2-covers.
  We find that the number of 2-covers, $s_n$, and proper 2-covers, $t_n$, on
$[n]$ both have asymptotic growth $$ s_n\sim t_n\sim
B_{2n}2^{-n}\exp(-\frac12\log(2n/\log n))= B_{2n}2^{-n}\sqrt{\frac{\log
n}{2n}}, $$ where $B_{2n}$ is the $2n$th Bell number, while the number of
restricted 2-covers, $u_n$, restricted, proper 2-covers on $[n]$, $v_n$, and
line graphs $l_n$, all have growth $$ u_n\sim v_n\sim l_n\sim
B_{2n}2^{-n}n^{-1/2}\exp(-[\frac12\log(2n/\log n)]^2). $$
  In our proofs we use probabilistic arguments for the unrestricted types of
2-covers and and generating function methods for the restricted types of
2-covers and line graphs.
