If G= (V (G), E (G) ) is a simple connected graph with vertex set V (G) and edge set E (G), we say that a subset D V (G) is a strong defensive alliance if for every vertex v D the condition D (v) ₃ (v) holds. The strong defensive alliance number (G) is defined as the minimum cardinality among all the strong defensive alliances. A unitary operator of graphs O assigns to each graph G a graph O (G). A few examples of unitary operators of graphs are: Subdivision S (G), R (G), Middle Q (G), Total T (G), and Central G. In this paper we determine the exact values of (S (G) ) and (R (G) ). We also characterize the graphs G for which the number of strong defensive alliances is 1, 2, or 3 in Q (G) and T (G). We also we give tight bounds for (S (G) ), (Q (G) ), (Q (G) ), (T (G) ), and (G).
Morales et al. (Wed,) studied this question.