BILANGAN DOMINASI-Xa DAN BILANGAN DOMINASI HIPER SEMIGRAF BIPARTIT

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ABSTRACT: Semigraph S is a pair (V,U) where V is a nonempty set whose elements are called vertices of S and U is a set of ordered n-tuples called edges of S. A Semigraph S called bipartite semigraph if its vertex set V can be partitioned into set {X,Y} such that X and Y are independent sets. A set D⊆X is a Xa-dominating set of S if ∀x∈X-D Xa-adjacent with v∈D. If there is not exist D_1⊂D is a Xa-dominating set such that D is a minimal Xa-dominating set of S and minimum cardinality of a minimal Xa-dominating set is called the Xa-domination number of  S and it is denoted by γ_Xa (S). A set D⊆X is a hyper dominating set of S if ∀y∈Y hyper dominated by x∈D. If there is not exist D_1⊂D is hyper dominating set such that D is a minimal hyper dominating set of S and minimum cardinality of a minimal hyper dominating set is called the hyper domination number of  S and it is denoted by γ_ha (S). The study in this thesis that γ_Xa (S) and γ_ha (S) are less than or equal to half of the number of vertices in vertex set X. Furthermore, studied application of Xa-domination number and hyper domination number for products of selling network in the insurance business.
Keywords: semigraph, bipartite semigraph, Xa-dominating set, Xa-domination number, hyper dominating set, hyper domination number
Penulis: Indah Permatasari, Djuwandi, Robertus Heri S.U
Kode Jurnal: jpmatematikadd150762

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Jp Matematika dd 2015