Minimal Graphs with Disjoint Dominating and Total Dominating Sets

Michael A. Henning; Jerzy Topp

doi:10.7151/dmgt.2433

Minimal Graphs with Disjoint Dominating and Total Dominating Sets

Michael A. Henning, Jerzy Topp

Mathematics and Applied Mathematics

State University of Applied Sciences

Research output: Contribution to journal › Article › peer-review

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-graphs without loops.

Original language	English
Journal	Discussiones Mathematicae - Graph Theory
DOIs	https://doi.org/10.7151/dmgt.2433
Publication status	Accepted/In press - 2021

Keywords

domination
total domination

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.7151/dmgt.2433

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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-graphs without loops.",

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year = "2021",

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language = "English",

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AU - Henning, Michael A.

AU - Topp, Jerzy

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AB - 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-graphs without loops.

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KW - total domination

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DO - 10.7151/dmgt.2433

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SN - 1234-3099

JO - Discussiones Mathematicae - Graph Theory

JF - Discussiones Mathematicae - Graph Theory

ER -

Minimal Graphs with Disjoint Dominating and Total Dominating Sets

Abstract

Keywords

ASJC Scopus subject areas

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