The diversity of domination

Michael A. Henning, Ortrud R. Oellermann, Henda C. Swart

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


For any graph G and a set ℋ of graphs, two distinct vertices of G are said to be ℋ-adjacent if they are contained in a subgraph of G which is isomorphic to a member of ℋ. A set 5 of vertices of G is an ℋ-dominating set (total ℋ-dominating set) of G if every vertex in V(G) - S (V(G), respectively) is ℋ-adjacent to a vertex in S. An ℋ-dominating set of G in which no two vertices are ℋ-adjacent in G is an ℋ-independent dominating set of G. The minimum cardinality of an ℋ-dominating set, total ℋ-dominating set and ℋ-independent dominating set of G is known as the ℋ-domination number, total ℋ-domination number, and ℋ-independent dominating number, of G, denoted, respectively, by γ(G), γtℋ(G), and i(G). We survey the applications and bounds obtained for the above domination parameters if ℋ={Kn} or ℋ = {Pi | 2 ≤ i ≤ n}, for an integer n ≥ 2.

Original languageEnglish
Pages (from-to)161-173
Number of pages13
JournalDiscrete Mathematics
Issue number1-3
Publication statusPublished - 5 Dec 1996
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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