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The paper probes the perfect dominating sets for a star Graph and how the construction of the family of set forms by using this perfect dominating set. This collection of families of sets becomes the on coefficient of novel perfect dominating polynomial. The relations which gets identified with this on coefficients helps to develop the perfect dominating polynomial. The properties of the polynomial is also mentioned.doi:10.26637/mjm0804/0071 fatcat:zue77nnvzjfzxgtyywq2wcmkuu