### 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 |*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.

#### Keywords

#### Full Text:

PDFDOI: http://dx.doi.org/10.5614/ejgta.2021.9.1.10

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