Let  be a simple graph. A dominating set  of  is a secure dominating set if for each  there exists  such that  is a dominating set. Let  be the centipede with  vertices and let  denote the family of all secure dominating sets of  with cardinality . Let . In this paper, we obtain recursive formula for . Using this recursive formula, we construct the polynomial,   which we call secure domination polynomial of   and obtain some properties of this polynomial.

Index Terms- domination, secure domination, secure domination number, secure dominating set, secure domination polynomial.

2010 Mathematics Subject Classification: 05C69,05C31