TOTAL AND PAIRED DOMINATION STABILITY IN PRISMS

Aleksandra Gorzkowska; Michael A. Henning; Monika Pilśniak; Elzbieta Tumidajewicz

doi:10.7151/dmgt.2421

TOTAL AND PAIRED DOMINATION STABILITY IN PRISMS

Aleksandra Gorzkowska, Michael A. Henning, Monika Pilśniak, Elzbieta Tumidajewicz

Mathematics and Applied Mathematics

AGH University of Science and Technology

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

1 Citation (Scopus)

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
Pages (from-to)	1147-1169
Number of pages	23
Journal	Discussiones Mathematicae - Graph Theory
Volume	43
Issue number	4
DOIs	https://doi.org/10.7151/dmgt.2421
Publication status	Published - 2023

Keywords

hypercube
paired domination stability
prism
total domination stability

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.7151/dmgt.2421

Cite this

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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 stγt(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.",

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

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T1 - TOTAL AND PAIRED DOMINATION STABILITY IN PRISMS

AU - Gorzkowska, Aleksandra

AU - Henning, Michael A.

AU - Pilśniak, Monika

AU - Tumidajewicz, Elzbieta

PY - 2023

Y1 - 2023

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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 stγt(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

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ER -

TOTAL AND PAIRED DOMINATION STABILITY IN PRISMS

Abstract

Keywords

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