Asymptotic Numbers of General 4-regular Graphs with given Connectivities
نویسنده
چکیده
Let g(n, l1, l2, d, t, q) be the number of general 4-regular graphs on n labelled vertices with l1 + 2l2 loops, d double edges, t triple edges and q quartet edges. We use inclusion and exclusion with five types of properties to determine the asymptotic behavior of g(n, l1, l2, d, t, q) and hence that of g(2n), the total number of general 4-regular graphs where l1, l2, d, t and q = o( √ n), respectively. We show that almost all general 4-regular graphs are 2-connected. Moreover, we determine the asymptotic numbers of general 4-regular graphs with given connectivities.
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تاریخ انتشار 2006