Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
433853 | Theoretical Computer Science | 2015 | 7 Pages |
Abstract
A theorem of Ore [20] states that if D is a minimal dominating set in a graph G=(V,E)G=(V,E) having no isolated nodes, then V−DV−D is a dominating set. It follows that such graphs must have two disjoint minimal dominating sets R and B. We describe a self-stabilizing algorithm for finding such a pair of sets. It also follows from Ore's theorem that in a graph with no isolates, one can find disjoint sets R and B where R is maximal independent and B is minimal dominating. We describe a self-stabilizing algorithm for finding such a pair. Both algorithms are described using the Distance-2 model, but can be converted to the usual Distance-1 model [7], yielding running times of O(n2m)O(n2m).
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Stephen T. Hedetniemi, David P. Jacobs, K.E. Kennedy,