### Abstract

Let G = (V, X) be a semigraph. A set D ⊆ V is called adjacent dominating set (ad-set) if for every υ ∈ V - D there exists a u ∈ D such that u is adjacent to v. The adjacency domination number γ_{a} = γ_{a}(G) is the minimum cardinality of an ad-set of G. Let V_{e} be the set of all end vertices in G. A set D ⊆ V_{e} is called end vertex adjacent dominating set (ead-set) if (i) D is an ad-set and (ii) Every end vertex υ ∈ V - D is e-adjacent to some end vertex u ∈ D in G. The end vertex adjacency domination number γ_{ea} = γ_{ea}(G) is the minimum cardinality of an ead-set of G. A set D C V is called consecutive adjacent dominating set (cad-set) if for every υ ∈ V - D there exists a u ∈ D such that u is ca-adjacent to v in G. The consecutive adjacency domination number γ_{ca} = γ_{ca}(G) is the minimum cardinality of a cad set of G. The above domination parameters are determined for various semigraphs and a few bounds are obtained.

Original language | English |
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Pages (from-to) | 106-111 |

Number of pages | 6 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 15 |

DOIs | |

Publication status | Published - 01-05-2003 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

*Electronic Notes in Discrete Mathematics*,

*15*, 106-111. https://doi.org/10.1016/S1571-0653(04)00548-7