Disjoint dominating and 2-dominating sets in graphs

Mateusz Miotk; Jerzy Topp; Paweł Żyliński

Disjoint dominating and 2-dominating sets in graphs

Combinatorics 2019-03-15 v1

Authors: Mateusz Miotk , Jerzy Topp , Paweł Żyliński

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.

Keywords

domination in graphs graph theory bipartite graphs

Cite

@article{arxiv.1903.06129,
  title  = {Disjoint dominating and 2-dominating sets in graphs},
  author = {Mateusz Miotk and Jerzy Topp and Paweł Żyliński},
  journal= {arXiv preprint arXiv:1903.06129},
  year   = {2019}
}

Comments

15 pages, 3 figures

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