Degree equitable restrained double domination in graphs

Sunilkumar M Hosamani (Rani Channamma University, India)
Shailaja Shirkol (Department of Mathematics, SDMCET, Dharwad, Karnataka, India)
Preeti B. Jinagouda (Department of Mathematics, SDMCET, Dharwad, Karnataka, India)
Marcin Krzywkowski (Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Poland)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 9, No 1 (2021): Electronic Journal of Graph Theory and Applications

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.