Let G=(V, E) be a undirected simple graph. Let P_n be the path with n vertices and let D_(Id) (P_n, i) be the family of interior dominating sets of G with cardinality. Let d_(Id)(P_n, i)=|D_(Id)(P_n, i)|. In this paper, we obtain a recursive formula for d_(Id)(P_n, i). Using this recursive formula, we construct the polynomial D_(Id)(p_n,x) = ∑_(i=|n/3|)~(n-2) d_(Id)(p_n, i)x~i, which we call interior domination polynomial of P_n and obtain some properties of this polynomial.
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