Degree equitable restrained double domination in graphs
| Main Authors: | Hosamani, Sunilkumar M; Rani Channamma University, India, Shirkol, Shailaja; Department of Mathematics, SDMCET, Dharwad, Karnataka, India, Jinagouda, Preeti B.; Department of Mathematics, SDMCET, Dharwad, Karnataka, India, Krzywkowski, Marcin; Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Poland |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2021
|
| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/445 https://www.ejgta.org/index.php/ejgta/article/view/445/pdf_165 |
Daftar Isi:
- A subset D ⊆ V(G) is called an equitable dominating set of a graph G if every vertex v ∈ V(G) \ D has a neighbor u ∈ D such that |dG(u)-dG(v)| ≤ 1. An equitable dominating set D is a degree equitable restrained double dominating set (DERD-dominating set) of G if every vertex of G is dominated by at least two vertices of D, and 〈V(G) \ D〉 has no isolated vertices. The DERD-domination number of G, denoted by γcl^e(G), is the minimum cardinality of a DERD-dominating set of G. We initiate the study of DERD-domination in graphs and we obtain some sharp bounds. Finally, we show that the decision problem for determining γcl^e(G) is NP-complete.