On the total domatic number of regular graphs
A set S of vertices of a graph G = (V;E) without isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domatic number of a graph G is the maximum number of total dominating sets into which the vertex set of G can be partitioned. We show that th...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Isfahan
2012-03-01
|
| Series: | Transactions on Combinatorics |
| Subjects: | |
| Online Access: | http://www.combinatorics.ir/?_action=showPDF&article=760&_ob=362cc9c41ad1def424bd149103450c49&fileName=full_text.pdf |
| Summary: | A set S of vertices of a graph G = (V;E) without isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domatic number of a graph G is the maximum number of total dominating sets into which the vertex set of G can be partitioned. We show that the total domatic number of a random r-regular graph is almost surely at most r |
|---|---|
| ISSN: | 2251-8657 2251-8665 |