Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THE EXPECTED INDEPENDENT DOMINATION NUMBER OF RANDOM DIRECTED ROOTED TREES

  • Published : 2004.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

We derive a formula for the expected value $\mu$(n) of the independent domination number of a random directed rooted tree with n labeled vertices and determine the asymptotic behavior of $\mu$(n) as n goes to infinity.

Keywords

References

  1. A. Cayley, On the analytical forms called trees, Philos. Mag. 28 (1858), 374–378. [Collected Mathematical Papers, Cambridge 4 (1891), 112–115.]
  2. G. Chartrand and L. Lesniak, Graphs & Digraphs, Wadsworth & Brooks, Monterey, 1986
  3. I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, New York, 1983
  4. K. Knopp, Infinite Sequences and Series, Dover, New York, 1956
  5. C. Lee, The expectation of independent domination number over random binary trees, Ars Combin. 56 (2000), 201–209
  6. A. Meir and J. W. Moon, The expected node-independence number of random trees, Proc. Kon. Ned. v. Wetensch 76 (1973), 335–341
  7. J. W. Moon, Counting Labelled Trees, Canadian Mathematical Congress, Montreal, 1970
  8. J. Riordan, Combinatorial Identities, Robert E. Krieger, New York, 1979
  9. N. J. A. Sloane and S. Plouffe, The Encyclopedia of Integer Sequences, Academic Press, San Diego, 1995