The number of dominating k-sets of paths, cycles and wheels

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We give a shorter proof of the recurrence relation for the domination polynomial γ(Pₙ,t) and for the number γₖ(Pₙ) of dominating k-sets of the path with n vertices. For every positive integers n and k, numbers γₖ(Pₙ) are determined solving a problem posed by S. Alikhani in CID 2015. Moreover, the numbers of dominating k-sets γₖ(Cₙ) of cycles and γₖ(Wₙ) of wheels with n vertices are computed.