secure domination number of generalized thorn graphs

A secure dominating set s ⊆ v is a dominating set of g satisfying the condition that for each u ∈ v s, there exists a vertex v ∈ n(u) ∩ s such that (s {v}) s {u} is a dominating set of g. the minimum cardinality of a secure dominating set of g is called the secure domination number of g, γs(g). in this paper, we obtain the secure domination number of generalized thorn paths, thorn graphs, and some special graph classes like thorn rod, thorn star and kragujevac trees, where the generalized thorn paths are important in the study of chemical compounds.