γ-Paired dominating graphs of lollipop, umbrella and coconut graphs
| Main Authors: | Eakawinrujee, Pannawat; Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand, Trakultraipruk, Nantapath; Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2023
|
| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/1476 https://www.ejgta.org/index.php/ejgta/article/view/1476/pdf_254 |
Daftar Isi:
- A paired dominating set of a graph G is a dominating set whose induced subgraph has a perfect matching. The paired domination number γpr(G) of G is the minimum cardinality of a paired dominating set. A paired dominating set D is a γpr(G)-set if |D|=γpr(G). The γ-paired dominating graph PDγ(G) of G is the graph whose vertex set is the set of all γpr(G)-sets, and two γpr(G)-sets D1 and D2 are adjacent in PDγ(G) if D2 = (D1 \ {u}) ∪ {v} for some u ∈ D1 and v ∉ D1. This paper determines the paired domination numbers of lollipop graphs, umbrella graphs, and coconut graphs. We also consider the γ-paired dominating graphs of those three graphs.