Domination Number of Vertex Amalgamation of Graphs

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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 G1, G2, ⋯, Gt 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 G1, G2, ⋯, Gt at vertex v. Based on the membership of the common vertex v in the γ ( Gi )-set, there exist three conditions to be considered. First, if v elements of every γ ( Gi )-set, second if there is no γ ( Gi )-set containing v, and third if either v is element of γ ( Gi )-set for 1 ≤ i ≤ p or there is no γ ( Gi )-set containing v for p < i ≤ t . For these three conditions, the domination number of G as vertex-amalgamation of G1, G2, ⋯, Gt at vertex v can be determined.

Original languageEnglish
Article number012059
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 12 Jun 2017
Event1st International Conference on Mathematics: Education, Theory, and Application, ICMETA 2016 - Surakarta, Indonesia
Duration: 6 Dec 20167 Dec 2016


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