Outer-restrained Domination in the Join and Corona of Graphs
Celart A. Tuble -, Enrico L. Enriquez · International Journal of Latest Engineering Research and Applications (IJLERA) · 2024
Let G be a connected simple graph.A set S ⊆ V G is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in V G ∖ S. A set S of vertices of a graph G is an outer-restrained dominating set if every vertex not in S is adjacent to some vertex in S and V G ∖ S is a restrained set.The outer-restrained domination number of G, denoted byγ r G is the minimum cardinality of an outer-restrained dominating set of G.An outer-restrained set of cardinality γ r G will be called γ r -set.In this paper, we initiate a study of the concept and give the characterization of the outer-restrained dominating set in the join and corona of two graphs.