# Disjoint dominating and 2-dominating sets in graphs

## TL;DR

This paper investigates the properties and computational complexity of graphs that contain disjoint dominating and 2-dominating sets, providing new characterizations and hardness results.

## Contribution

It introduces characterizations and complexity results for $DD_2$-graphs, advancing understanding of their structural and computational properties.

## Key findings

- Characterizations of $DD_2$-graphs
- Hardness results for recognizing $DD_2$-graphs
- Insights into the structure of disjoint dominating sets

## Abstract

A graph $G$ is a $D\!D_2$-graph if it has a pair $(D,D_2)$ of disjoint sets of vertices of $G$ such that $D$ is a dominating set and $D_2$ is a 2-dominating set of $G$. We provide several characterizations and hardness results concerning $D\!D_2$-graphs.