Degree equitable restrained double domination in graphs
Sunilkumar M. Hosamani, Shailaja S. Shirkol, Preeti B. Jinagouda, Marcin Krzywkowski · Electronic Journal of Graph Theory and Applications · 2021
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 | d G ( u )- d G ( 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 γ cl ^ 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 γ cl ^ e ( G ) is NP-complete.