On the (signless) Laplacian spectral characterization of the line graphs of lollipop graphs

Let denote the lollipop graph on n vertices obtained by identifying a vertex of the cycle Cg of order g and an end vertex of the path Pk+1 of order k+1. In this paper we prove that all line graphs of lollipop graphs are determined by their Laplacian spectrum. Furthermore, we show that all but the case that g=k⩾3 are determined by their signless Laplacian spectrum, and also give the Q-cospectral class of .