Journal of the
Korean Mathematical Society JKMS

Let $g(2n,l,d)$ be the number of general cubic graphs on $2n$ labeled vertices with $l$ loops and $d$ double edges. We use inclusion and exclusion with two types of properties to determine the asymptotic behavior of $g(2n,l,d)$ and hence that of $g(2n)$, the total number of general cubic graphs of order $2n$. We show that almost all general cubic graphs are connected. Moreover, we determined the asymptotic numbers of general cubic graphs with given connectivity.

Keywords: inclusion and exclusion, general cubic graphs, asymptotic number

MSC numbers: Primary 05A16, 05A20