Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ASYMPTOTIC NUMBERS OF GENERAL 4-REGULAR GRAPHS WITH GIVEN CONNECTIVITIES

  • Published : 2006.02.01
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Abstract

Let $g(n,\;l_1,\;l_2,\;d,\;t,\;q)$ be the number of general4-regular graphs on n labelled vertices with $l_1+2l_2$ 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 $g(n,\;l_1,\;l_2,\;d,\;t,\;q)$ and hence that of g(2n), the total number of general 4-regular graphs where $l_1,\;l_2,\;d,\;t\;and\;q\;=\;o(\sqrt{n})$, 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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References

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