Let \(G=(V(G),E(G))\) be a simple graph of order n. A set \(S\subseteq V(G)\) is said to be a restrained dominating set if each vertex in \(V(G)-S\) is adjacent to a vertex in S and to a vertex in \(V(G)-S\) . The restrained domination polynomial of a graph G is defined by \(D_{r}(G,x)=\sum \limits _{i=\gamma _{r}(G)}^{n}d_{r}(G,i)x^{i}\) where \(d_{r}(G,i)\) is the number of restrained dominating sets of G of size i and \(\gamma _{r}(G)\) is the restrained domination number of a graph G. In this paper we derive some recurrence relations for \(D_{r}(G,x)\) .
