Abstract
A global defensive alliance in a graph G = (V,E) is a dominating set S satisfying the condition that for every vertex v ∈ S, |N[v] ∩ S| ≥ |N(v) ∩ (V - S)|. In this note, a new upper bound on the global defensive alliance number of a tree is given in terms of its order and the number of support vertices. Moreover, we characterize trees attaining this upper bound.
| Original language | English |
|---|---|
| Pages (from-to) | 1-7 |
| Number of pages | 7 |
| Journal | Electronic Journal of Combinatorics |
| Volume | 18 |
| Issue number | 1 |
| Publication status | Published - 2011 |
Scopus Subject Areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics
User-Defined Keywords
- Global defensive alliance number
- Tree
- Upper bound