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On the Paired-Domination Subdivision Number of Trees
| Content Provider | MDPI |
|---|---|
| Author | Wei, Shouliu Hao, Guoliang Sheikholeslami, Seyed Khoeilar, Rana Karami, Hossein |
| Copyright Year | 2021 |
| Description | A paired-dominating set of a graph G without isolated vertices is a dominating set of vertices whose induced subgraph has perfect matching. The minimum cardinality of a paired-dominating set of G is called the paired-domination number $γ_{pr}$(G) of G. The paired-domination subdivision number $sd_{γpr}$(G) of G is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the paired-domination number. Here, we show that, for each tree T ≠ $P_{5}$ of order n ≥ 3 and each edge e ∉ E(T), $sd_{γpr}$(T) + $sd_{γpr}$(T + e) ≤ n + 2. |
| Starting Page | 1135 |
| e-ISSN | 22277390 |
| DOI | 10.3390/math9101135 |
| Journal | Mathematics |
| Issue Number | 10 |
| Volume Number | 9 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2021-05-17 |
| Access Restriction | Open |
| Subject Keyword | Mathematics Logic Paired-domination Number Paired-domination Subdivision Number |
| Content Type | Text |
| Resource Type | Article |
