$Kite_{p+2,p}$ is determined by its Laplacian spectrum

Abstract

$Kite_{n,p}$ denotes the kite graph that is obtained by appending complete graph with order $pgeq4$ to an endpoint of path graph with order $n-p$‎. ‎It is shown that $Kite_{n,p}$ 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 $Kite_{n,p}$ is determined by its signless Laplacian spectrum when $ngeq4$‎, ‎$nneq5$ and is also determined by its distance spectrum when $ngeq4$ [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 $Kite_{n,p}$ is determined by its Laplacian spectrum for $n-pleq2$‎.