Let G=(V,E) be a simple graph. A dominating set of G is a subset
DβV such that every vertex not in D is adjacent to at least one
vertex in D. The cardinality of a smallest dominating set of G, denoted by
Ξ³(G), is the domination number of G. A dominating set D is called a
secure dominating set of G, if for every uβVβD, there exists a vertex
vβD such that uvβE and Dβ{v}βͺ{u} is a dominating set of
G. The cardinality of a smallest secure dominating set of G, denoted by
Ξ³sβ(G), is the secure domination number of G. For any kβN, the k-subdivision of G is a simple graph Gk1β
which is constructed by replacing each edge of G with a path of length k.
In this paper, we study the secure domination number of k-subdivision of G.Comment: 10 Pages, 8 Figure