Total domination good vertices in graphs

Teresa W. Haynes, Michael A. Henning

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The total domination number γt(G) is the minimum cardinality of a total dominating set of G. A vertex that is contained in some minimum total dominating set of a graph G is a good vertex, otherwise it is a bad vertex. We determine for which triples (x, y, z) there exists a connected graph G with γt(G) = x and with y good vertices and z bad vertices, and we give graphs realizing these triples.

Original languageEnglish
Pages (from-to)305-315
Number of pages11
JournalAustralasian Journal of Combinatorics
Publication statusPublished - 2002
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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