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

Let H-g,k(n) denote the lollipop graph on n vertices obtained by identifying a vertex of the cycle C-g 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 L(H-g,k(n)) of lollipop graphs are determined by their Laplacian spectrum. Furthermore, we show that all L(H-g,k(n)) but the case that g = k >= 3 are determined by their signless Laplacian spectrum, and also give the Q-cospectral class of L(H-g,k(n)) (r >= 3). (C) 2013 Elsevier Inc. All rights reserved.