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Abstract
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A graph G is said to be (DLS) DQS if there is no other non-isomorphic graph with the same
(Laplacian spectrum) signless Laplacian spectrum as G. A sun graph SG(p) is obtained by
appending a pendant vertex to any vertices of a cycle Cp and a broken sun graph BSG(p, q) is
a graph obtained by deleting p − q pendant vertices of a sun SG(p). We obtain some results
related to the graphs that their signless Laplacian eigenvalues are the same as the signless
Laplacian eigenvalues of a broken sun graph.
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