Abstract.Let 𝐺 be a simple graph of order 𝑛. The domination polynomial of 𝐺 is the polynomial D(G,x)= ∑ i=0 n d(G,i) x i , where 𝑑(𝐺,𝑖) is the number of dominating sets of 𝐺 of size 𝑖. Let 𝑛 ...

Abstract. A graph is said to be DQS if there is no other non-isomorphic graph with the same signless Laplacian spectrum. For a DQS graph 𝐺, we show that 𝐺∪𝑟𝐾₁ is DQS under certain conditions.