Minimal Graphs with Disjoint Dominating and Paired-Dominating Sets
A subset D ⊆ VG is a dominating set of G if every vertex in VG – D has a neighbor in D, while D is a paired-dominating set of G if D is a dominating set and the subgraph induced by D contains a perfect matching. A graph G is a DPDP -graph if it has a pair (D, P) of disjoint sets of vertices of G suc...
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2021-08-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.2328 |
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doaj-2863f0bd427643679140db0d55e1eb832021-09-05T17:20:25ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922021-08-0141382784710.7151/dmgt.2328Minimal Graphs with Disjoint Dominating and Paired-Dominating SetsHenning Michael A.0Topp Jerzy1Department of Pure and Applied Mathematics, University of Johannesburg, Auckland Park 2006, South AfricaThe State University of Applied Sciences in Elbląg,PolandA subset D ⊆ VG is a dominating set of G if every vertex in VG – D has a neighbor in D, while D is a paired-dominating set of G if D is a dominating set and the subgraph induced by D contains a perfect matching. A graph G is a DPDP -graph if it has a pair (D, P) of disjoint sets of vertices of G such that D is a dominating set and P is a paired-dominating set of G. The study of the DPDP -graphs was initiated by Southey and Henning [Cent. Eur. J. Math. 8 (2010) 459–467; J. Comb. Optim. 22 (2011) 217–234]. In this paper, we provide conditions which ensure that a graph is a DPDP -graph. In particular, we characterize the minimal DPDP -graphs.https://doi.org/10.7151/dmgt.2328dominationpaired-domination05c6905c85 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Henning Michael A. Topp Jerzy |
| spellingShingle |
Henning Michael A. Topp Jerzy Minimal Graphs with Disjoint Dominating and Paired-Dominating Sets Discussiones Mathematicae Graph Theory domination paired-domination 05c69 05c85 |
| author_facet |
Henning Michael A. Topp Jerzy |
| author_sort |
Henning Michael A. |
| title |
Minimal Graphs with Disjoint Dominating and Paired-Dominating Sets |
| title_short |
Minimal Graphs with Disjoint Dominating and Paired-Dominating Sets |
| title_full |
Minimal Graphs with Disjoint Dominating and Paired-Dominating Sets |
| title_fullStr |
Minimal Graphs with Disjoint Dominating and Paired-Dominating Sets |
| title_full_unstemmed |
Minimal Graphs with Disjoint Dominating and Paired-Dominating Sets |
| title_sort |
minimal graphs with disjoint dominating and paired-dominating sets |
| publisher |
Sciendo |
| series |
Discussiones Mathematicae Graph Theory |
| issn |
2083-5892 |
| publishDate |
2021-08-01 |
| description |
A subset D ⊆ VG is a dominating set of G if every vertex in VG – D has a neighbor in D, while D is a paired-dominating set of G if D is a dominating set and the subgraph induced by D contains a perfect matching. A graph G is a DPDP -graph if it has a pair (D, P) of disjoint sets of vertices of G such that D is a dominating set and P is a paired-dominating set of G. The study of the DPDP -graphs was initiated by Southey and Henning [Cent. Eur. J. Math. 8 (2010) 459–467; J. Comb. Optim. 22 (2011) 217–234]. In this paper, we provide conditions which ensure that a graph is a DPDP -graph. In particular, we characterize the minimal DPDP -graphs. |
| topic |
domination paired-domination 05c69 05c85 |
| url |
https://doi.org/10.7151/dmgt.2328 |
| work_keys_str_mv |
AT henningmichaela minimalgraphswithdisjointdominatingandpaireddominatingsets AT toppjerzy minimalgraphswithdisjointdominatingandpaireddominatingsets |
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