Total and paired domination stability in prisms

Aleksandra Gorzkowska; Michael A. Henning; Monika Pilśniak; Elz Bieta Tumidajewicz

doi:10.7151/dmgt.2421

Total and paired domination stability in prisms

Aleksandra Gorzkowska, Michael A. Henning, Monika Pilśniak, Elz Bieta Tumidajewicz

Mathematics and Applied Mathematics

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

Abstract

A set D of vertices in an isolate-free graph is a total dominating set if every vertex is adjacent to a vertex in D. If the set D has the additional property that the subgraph induced by D contains a perfect matching, then D is a paired dominating set of G. The total domination number γ_t(G) and the paired domination number γ_pr(G) of a graph G are the minimum cardinalities of a total dominating set and a paired dominating set of G, respectively. The total domination stability (respectively, paired domination stability) of G, denoted st _γt(G) (respectively, st_γpr(G)), is the minimum size of a non-isolating set of vertices in G whose removal changes the total domination number (respectively, paired domination number). In this paper, we study total and paired domination stability in prisms.

Original language	English
Journal	Discussiones Mathematicae - Graph Theory
DOIs	https://doi.org/10.7151/dmgt.2421
Publication status	Accepted/In press - 2021

Keywords

Hypercube
Paired domination stability
Prism
Total domination stability

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.7151/dmgt.2421

Cite this

@article{30542fe243a641329529d7aa77d9b866,

title = "Total and paired domination stability in prisms",

abstract = "A set D of vertices in an isolate-free graph is a total dominating set if every vertex is adjacent to a vertex in D. If the set D has the additional property that the subgraph induced by D contains a perfect matching, then D is a paired dominating set of G. The total domination number γt(G) and the paired domination number γpr(G) of a graph G are the minimum cardinalities of a total dominating set and a paired dominating set of G, respectively. The total domination stability (respectively, paired domination stability) of G, denoted st γt(G) (respectively, stγpr(G)), is the minimum size of a non-isolating set of vertices in G whose removal changes the total domination number (respectively, paired domination number). In this paper, we study total and paired domination stability in prisms.",

keywords = "Hypercube, Paired domination stability, Prism, Total domination stability",

author = "Aleksandra Gorzkowska and Henning, {Michael A.} and Monika Pil{\'s}niak and Tumidajewicz, {Elz Bieta}",

year = "2021",

doi = "10.7151/dmgt.2421",

language = "English",

journal = "Discussiones Mathematicae - Graph Theory",

issn = "1234-3099",

publisher = "University of Zielona Gora",

}

TY - JOUR

T1 - Total and paired domination stability in prisms

AU - Gorzkowska, Aleksandra

AU - Henning, Michael A.

AU - Pilśniak, Monika

AU - Tumidajewicz, Elz Bieta

PY - 2021

Y1 - 2021

N2 - A set D of vertices in an isolate-free graph is a total dominating set if every vertex is adjacent to a vertex in D. If the set D has the additional property that the subgraph induced by D contains a perfect matching, then D is a paired dominating set of G. The total domination number γt(G) and the paired domination number γpr(G) of a graph G are the minimum cardinalities of a total dominating set and a paired dominating set of G, respectively. The total domination stability (respectively, paired domination stability) of G, denoted st γt(G) (respectively, stγpr(G)), is the minimum size of a non-isolating set of vertices in G whose removal changes the total domination number (respectively, paired domination number). In this paper, we study total and paired domination stability in prisms.

AB - A set D of vertices in an isolate-free graph is a total dominating set if every vertex is adjacent to a vertex in D. If the set D has the additional property that the subgraph induced by D contains a perfect matching, then D is a paired dominating set of G. The total domination number γt(G) and the paired domination number γpr(G) of a graph G are the minimum cardinalities of a total dominating set and a paired dominating set of G, respectively. The total domination stability (respectively, paired domination stability) of G, denoted st γt(G) (respectively, stγpr(G)), is the minimum size of a non-isolating set of vertices in G whose removal changes the total domination number (respectively, paired domination number). In this paper, we study total and paired domination stability in prisms.

KW - Hypercube

KW - Paired domination stability

KW - Prism

KW - Total domination stability

UR - http://www.scopus.com/inward/record.url?scp=85112378499&partnerID=8YFLogxK

U2 - 10.7151/dmgt.2421

DO - 10.7151/dmgt.2421

M3 - Article

AN - SCOPUS:85112378499

SN - 1234-3099

JO - Discussiones Mathematicae - Graph Theory

JF - Discussiones Mathematicae - Graph Theory

ER -

Total and paired domination stability in prisms

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this