## Abstract

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_{ℋ}(G), γ^{t}ℋ(G), and i_{ℋ}(G). We survey the applications and bounds obtained for the above domination parameters if ℋ={K_{n}} or ℋ = {P_{i} | 2 ≤ i ≤ n}, for an integer n ≥ 2.

Original language | English |
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Pages (from-to) | 161-173 |

Number of pages | 13 |

Journal | Discrete Mathematics |

Volume | 161 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 5 Dec 1996 |

Externally published | Yes |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics