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Abstract
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Two graphs are said to be Q-cospectral if they have the same signless Laplacian spectrum. A graph is said to be DQS if
there are no other nonisomorphic graphs Q-cospectral with it. A tree is called double starlike if it has exactly two vertices
of degree greater than 2. Let Hn(p, q) with n \geq 2, p \geq q \geq 2 denote the double starlike tree obtained by attaching p
pendant vertices to one pendant vertex of the path Pn and q pendant vertices to the other pendant vertex of Pn. In this
paper, we prove that Hn(p, q) is DQS for n \geq 2, p \geq q \geq 2
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