Split Geodetic Dominating Sets in Path Graphs

Abstract

Let  be the family of split geodetic dominating sets of the path graph . with cardinality i and let . Then the split geodetic polynomial  of  is defined as  = , where  is the split geodetic domination number of .In this paper we have determined the family of split geodetic dominating sets of the path graph  with cardinality .Also , we have obtained the recursive formula to derive the split geodetic domination polynomials of paths and also obtain some properties of this polynomial.