Papers › Paired domination in trees: A linear algorithm and asymptotic normality
Paired domination in trees: A linear algorithm and asymptotic normality
Michael A. Henning, Dimbinaina Ralaivaosaona
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as an induced subgraph). The paired domination number, γₚᵣ(G), of G is the minimum cardinality of a paired dominating set of G. We present a linear algorithm for computing the paired domination number of a tree. As an application of our algorithm, we prove that the paired domination number is asymptotically normal in a random rooted tree of order n generated by a conditioned Galton-Watson process as n→∞. In particular, we have found that the paired domination number of a random Cayley tree of order n, where each tree is equally likely, is asymptotically normal with expectation approaching (0.5177…)n.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections