THE EXPECTED INDEPENDENT DOMINATION NUMBER OF RANDOM DIRECTED ROOTED TREES

Title & Authors
THE EXPECTED INDEPENDENT DOMINATION NUMBER OF RANDOM DIRECTED ROOTED TREES
Song, Jun-Ho; Lee, Chang-Woo;

Abstract
We derive a formula for the expected value $\small{\mu}$(n) of the independent domination number of a random directed rooted tree with n labeled vertices and determine the asymptotic behavior of $\small{\mu}$(n) as n goes to infinity.
Keywords
independence number;domination number;independent domination number;random directed rooted tree;expected value;
Language
English
Cited by
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