## Abstract

For a graph G = (V, E), a subset S of V is called a dominating set if every vertex x in V is either in S or adjacent to a vertex in S. The domination number γ ( G ) is the minimum cardinality of the dominating set of G. The dominating set of G with a minimum cardinality denoted by γ ( G )-set. Let G_{1}, G_{2}, ⋯, G_{t} be subgraphs of the graph G. If the union of all these subgraphs is G and their intersection is {v}, then we say that G is the vertex-amalgamation of G_{1}, G_{2}, ⋯, G_{t} at vertex v. Based on the membership of the common vertex v in the γ ( G_{i} )-set, there exist three conditions to be considered. First, if v elements of every γ ( G_{i} )-set, second if there is no γ ( G_{i} )-set containing v, and third if either v is element of γ ( G_{i} )-set for 1 ≤ i ≤ p or there is no γ ( G_{i} )-set containing v for p < i ≤ t . For these three conditions, the domination number of G as vertex-amalgamation of G_{1}, G_{2}, ⋯, G_{t} at vertex v can be determined.

Original language | English |
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Article number | 012059 |

Journal | Journal of Physics: Conference Series |

Volume | 855 |

Issue number | 1 |

DOIs | |

Publication status | Published - 12 Jun 2017 |

Event | 1st International Conference on Mathematics: Education, Theory, and Application, ICMETA 2016 - Surakarta, Indonesia Duration: 6 Dec 2016 → 7 Dec 2016 |