We show that any tree that has a universal minimal total dominating function has one which only takes 0-1 values. K 3 demonstrates that this fails for graphs in general. Given a graph G =(V, E), for each vertex ve V let F(v) be the set of its neighbours (in particular, not including v itself). A to
Trees having many minimal dominating sets
โ Scribed by Krzywkowski, Marcin
- Book ID
- 120245118
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 148 KB
- Volume
- 113
- Category
- Article
- ISSN
- 0020-0190
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The relation Ye on the set of minimal dominating functions (MDFs) of a finite graph G is defined by f&?g if and only if any convex combination off and g is also an MDF. If fis a nonintegral MDF of a tree, the existence of another MDF with fewer nonintegral values and other desirable properties is es
For a subset W of vertices of an undirected graph G, let S(W) be the subgraph consisting of W, all edges incident to at least one vertex in W, and all vertices adjacent to at least one vertex in W. If there exists a W such that S(W) is a tree containing all the vertices of G, then S(W) is a spanning