Enrico Enriquez, Valerie Fernandez, Teodora Punzalan, Jonecis Dayap
Let G be a connected simple graph. A dominating set P ⊆ 7(G) is called a perfect dominating set of G if each u ∈ 7(G) \ S is dominated by exactly one element of S. A set S of vertices of a graph G is an outer-connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraph induced by 7(G) \ S is connected. A perfect dominating set S of a graph G is a perfect outer-connected dominating set if the subgraph induced by 7(G) \ S is connected. The perfect outer-connected domination number of G, denoted by yc p(G), is the smallest cardinality of a perfect outer-connected dominating set S of G. A perfect outer-connected dominating set with cardinality ÿc p (G) is called yc p -set of G. In this paper, we will show that given positive integers, a, b, c, and n such that a ≤ b ≤ c < n — 1, there exists a connected graph G with |7(G)| = n, y(G) = a,yp(G) = b, and ÿc p(G) = c. Further, we give the characterization of the perfect outer-connected dominating set of the join and corona of two graphs and give their corresponding perfect outer-connected domination number. © 2016, University of San Jose-Recoletos. All rights reserved.
University of San Carlos, Philippines; University of San Jose-Recoletos, Philippines
