Total and paired domination stability in prisms

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

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
JournalDiscussiones Mathematicae - Graph Theory
Publication statusAccepted/In press - 2021


  • Hypercube
  • Paired domination stability
  • Prism
  • Total domination stability

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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