Efficient dominating sets in labeled rooted oriented trees

The Number of Independent Dominating Sets of Labeled Trees

We count the numbers of independent dominating sets of rooted labeled trees, ordinary labeled trees, and recursive trees, respectively.

Visualising Populations of Rooted Labeled Trees ona

Efficient Generation of Rooted Trees

In this paper we give an algorithm to generate all rooted trees with at most n vertices. The algorithm generates each tree in constant time on average. Furthermore the algorithm is simple, and clarifies a simple relation among the trees, that is a family tree of trees, and outputs trees based on the relation.

Minimal 2-dominating sets in trees

We provide an algorithm for listing all minimal 2-dominating sets of a tree of order n in time O(1.3248n). This implies that every tree has at most 1.3248n minimal 2-dominating sets. We also show that this bound is tight.

Minimal Double Dominating Sets in Trees

We provide an algorithm for listing all minimal double dominating sets of a tree of order n in time O(1.3248). This implies that every tree has at most 1.3248 minimal double dominating sets. We also show that this bound is tight.