Disjoint Restrained Domination in the Join and Corona of Graphs

**MLA Style: **Stephen Paul G. Cajigas, Enrico L. Enriquez, Grace M. Estrada, Katrina E. Belleza, Carmelita M. Loquias. "Disjoint Restrained Domination in the Join and Corona of Graphs" International Journal of Mathematics Trends and Technology 67.12 (2021):57-61.

**APA Style: **Stephen Paul G. Cajigas, Enrico L. Enriquez, Grace M. Estrada, Katrina E. Belleza, Carmelita M. Loquias(2021). Disjoint Restrained Domination in the Join and Corona of Graphs International Journal of Mathematics Trends and Technology, 67(12), 57-61.

**Abstract**

Let G = (V(G), E(G)) be a connected simple graph. A subset S of V(G) is a dominating set of G if for every u ∈ V(G\S), there exists v ∈ S such that uv ∈ E(G). A dominating set D is called a restrained dominating set if for each u ∈ V(G)\D there exists v ∈ V(D) and z ∈ V(G)\D(z ≠ u) such that u is adjacent to v and z. Further, if D is a minimum restrained dominating set of G, then a restrained dominating set S ⊆ V(G)\D is called an inverse restrained dominating set of G with respect to D. A disjoint restrained dominating set of G is the set C = D ∪ S ⊆ V(G). In this paper, we investigate the concept and give some important results on disjoint restrained domination arising from the join and corona of two graphs.

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**Keywords : **binary operations on graphs, disjoint restrained dominating set, dominating set, inverse restrained dominating set, restrained dominating set.