Enrico L. Enriquez, Sergio R. Canoy
In this paper, we give necessary and sufficient conditions for a subset S of the vertex set of a connected graph G to be a secure convex dominating set. Some realization problems will be given. In particular, we show that given positive integers k and n such that n ≥ 4 and 1 ≤ k ≤ n, there exists a connected graph G with |V (G)| = n and γscon(G) = k. Also, we show that for any positive integers k, m and n such that 1 ≤ k ≤ m - 2 and m ≤ n, there exists a connected graph G with |V (G)| = n, γscon(G) = m, and γcon(G) = k. © 2015.
Department of Mathematics, College of Arts and Sciences, University of San Carlos, Cebu City, 6000, Philippines; Department of Mathematics and Statistics, Mindanao State University-Iligan Institute of Technology, Tibanga Highway, Iligan City, 9200, Philippines
