Abstract
Let G = (V(G), E(G)) be a graph with δ(G) ≥ 1. A set D ⊆ V(G) is a paired-dominating set if D is a dominating set and the induced subgraph G[D] contains a perfect matching. The paired domination number of G, denoted by γP(G), is the minimum cardinality of a paired-dominating set of G. The paired bondage number, denoted by bp(G), is the minimum cardinality among all sets of edges E′ ⊆ E such that δ(G - E′) ≥1 and γp(G - E′) > γp(G). For any bp(G) edges E′ ⊆ E with δ(G - E′) ≥ 1, if γp(G - E′) > γp(G), then G is called uniformly pair-bonded graph. In this paper, we prove that there exists uniformly pair-bonded tree T with bp(T) = k for any positive integer k. Furthermore, we give a constructive characterization of uniformly pair-bonded trees.
| Original language | English |
|---|---|
| Pages (from-to) | 71-78 |
| Number of pages | 8 |
| Journal | Ars Combinatoria |
| Volume | 94 |
| Publication status | Published - Jan 2010 |
Scopus Subject Areas
- General Mathematics
User-Defined Keywords
- Domination number
- Paired bondage number
- Paired-domination num-ber
- Uniformly pairbonded graph