Total domination changing and stable graphs upon vertex removal

Wyatt J. Desormeaux, Teresa W. Haynes, Michael A. Henning

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

A set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. A graph is total domination vertex removal stable if the removal of an arbitrary vertex leaves the total domination number unchanged. On the other hand, a graph is total domination vertex removal changing if the removal of an arbitrary vertex changes the total domination number. In this paper, we study total domination vertex removal changing and stable graphs.

Original languageEnglish
Pages (from-to)1548-1554
Number of pages7
JournalDiscrete Applied Mathematics
Volume159
Issue number15
DOIs
Publication statusPublished - 6 Sept 2011

Keywords

  • Total domination
  • Vertex removal changing
  • Vertex removal stable

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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