Degree equitable restrained double domination in graphs

Abstract

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.

Keywords

• domination, degree equitable domination, derd-domination