• S.CHANDRASEKARAN
• K.KANIMOZHI

Let G=(V,E) be a connected simple undirected graph. A subset S⊆V is a dominating set if for every vertex v∈V/S, there exists a vertex w∈S such that vw∈E; that is every vertex outside S has atleast one neighbor in S. The minimum cardinality of a dominating set of G is the domination number of G, it is denoted by γ(G). A subset S⊆V is a perfect dominating set if for every vertex v∈V/S, there exists exactly one vertex w∈S such that vw∈E; that is every vertex outside S has exactly one neighbor in S. The minimum cardinality of a perfect dominating set of G is the perfect domination number of G, it is denoted by γ_p (G). We introduce new concept that a perfect domination polynomial of a graph G. The perfect domination polynomial of a graph G of order n is the polynomial PD(G,x)=∑_(i=γ_p (G))^n▒〖pd(G,i)x^i 〗 Where pd(G,i) is the number of perfect dominating sets of G of size i and γ_p (G) is the perfect domination number of G. we obtain some properties of D(G,x) and also derive the domination under graph operations namely union, intersection and cartesian product

Domination set, Domination polynomial, Lollipop graph, Perfect domination, Perfect domination polynomial.

"PERFECT DOMINATION POLYNOMIAL UNDER GRAPH OPERATIONS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 4, page no.380-383, April-2019, Available :http://www.jetir.org/papers/JETIR1904I64.pdf

"PERFECT DOMINATION POLYNOMIAL UNDER GRAPH OPERATIONS", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 4, page no. pp380-383, April-2019, Available at : http://www.jetir.org/papers/JETIR1904I64.pdf