Let  be a simple graph. A dominating set  is a strong split dominating set if the induced subgraph  is totally disconnected with at least two vertices. Let  be the family of strong split dominating sets of  of cardinality  and .  We define the strong split domination polynomial of a graph  of order  as the polynomial . In this paper, we determine the strong split domination polynomial of cycles and obtain some of its properties.

Keywords and Phrases: Strong split dominating set, Strong split domination polynomial.

2010 Mathematics Subject Classification: 05C69