On the domination polynomials of cactus chains

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Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G, x)=∑ᵢ₌ᵧ₍G₎ⁿ d(G,i) xⁱ, where d(G,i) is the number of dominating sets of G of size i and γ(G) is the domination number of G. In this paper we consider cactus chains with triangular and square blocks and study their domination polynomials.