Kitep+2,p is determined by its Laplacian spectrum

Kiten,p denotes the kite graph that is obtained by appending complete graph with order p≥4 to an endpoint of path graph with order n−p. It is shown that Kiten,p is determined by its adjacency spectrum for all p and n [H. Topcu and S. Sorgun, The kite graph is determined by its adjacency spectrum, Applied Math. and Comp., 330 (2018) 134--142]. For n−p=1, it is proven that Kiten,p is determined by its signless Laplacian spectrum when n≥4, n≠5 and is also determined by its distance spectrum when n≥4 [K. C. Das and M. Liu, Kite graphs are determined by their spectra, Applied Math. and Comp., 297 (2017) 74--78]. In this note, we say that Kiten,p is determined by its Laplacian spectrum for n−p≤2.