The paper illustrates algebraic representation of the friendship Graph $F_n$ and corona of $G$ and $K_1$ called the Perfect dominating polynomial. The Perfect dominating polynomial is constructed by using Perfect dominating set. At first we find the family Perfect dominating set with the given cardinality. The collection of families of sets become the coefficient of novel Perfect dominating polynomial. The relations which gets identified with this on coefficients helps to develop the Perfect dominating polynomial of $F_n$ and $G ∘ K_1$ thus we find the roots of this polynomial.