Minimal graphs with disjoint dominating and total dominating sets

Michael A. Henning; Jerzy Topp

Minimal graphs with disjoint dominating and total dominating sets

Combinatorics 2021-03-05 v2

Authors: Michael A. Henning , Jerzy Topp

Abstract

A graph $G$ is a DTDP-graph if it has a pair $(D,T)$ of disjoint sets of vertices of $G$ such that $D$ is a dominating set and $T$ is a total dominating set of $G$ . Such graphs were studied in a number of research papers. In this paper we study further properties of DTDP-graphs and, in particular, we characterize minimal DTDP-gaphs without loops.

Keywords

domination in graphs graph theory graph theory of groups

Cite

@article{arxiv.2101.06247,
  title  = {Minimal graphs with disjoint dominating and total dominating sets},
  author = {Michael A. Henning and Jerzy Topp},
  journal= {arXiv preprint arXiv:2101.06247},
  year   = {2021}
}

Comments

23 pages, 12 figures

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