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
Pages (from-to)	47-74
Number of pages	28
Journal	Discussiones Mathematicae - Graph Theory
Volume	44
Issue number	1
DOIs	https://doi.org/10.7151/dmgt.2433
Publication status	Published - 2024

Keywords

domination
total domination

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.7151/dmgt.2433

Cite this

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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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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

UR - https://www.scopus.com/pages/publications/85117402162

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DO - 10.7151/dmgt.2433

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JO - Discussiones Mathematicae - Graph Theory

JF - Discussiones Mathematicae - Graph Theory

IS - 1

ER -

MINIMAL GRAPHS WITH DISJOINT DOMINATING AND TOTAL DOMINATING SETS

Abstract

Keywords

ASJC Scopus subject areas

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